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We compare the spatial distributions of galaxy clusters in the northern and
southern galactic hemispheres, and the Abell and ACO clusters distributions. We
perform a statistical (correlation and cluster) analysis of a sample of Abell
and ACO galaxy clusters in the southern galactic hemisphere. We compare these
results with a symmetric sample at northern galactic latitude taken from
Postman et al. (1992). For the northern sample, we substantially confirm the
results of Postman et al. We find that the two-point spatial correlation
function of northern and southern clusters is comparable, with mean correlation
length 19.6 Mpc and slope -1.8 positive up to about 45 Mpc. Percolation
properties are remarkably similar in the northern and southern cluster samples.
We give also a catalog of superclusters. In the south galactic hemisphere the
main feature is a very rich, extended supercluster in the Horologium region at
a redshift 0.06, near to a large void.
|
astro-ph/9205004
| 727,326 |
The interplay between the chiral anomaly and the non-leptonic weak
Hamiltonian is studied. The structure of the corresponding effective Lagrangian
of odd intrinsic parity is established. It is shown that the factorizable
contributions (leading in $1/N_C$) to that Lagrangian can be calculated without
free parameters. As a first application, the decay $K^+ \ra \pi^+ \pi^0 \gamma$
is investigated.
|
hep-ph/9205210
| 727,326 |
We apply methods developed by Lovelace, Lipatov and Kirschner to evaluate the
leading Regge trajectories \alpha(t) with the quantum numbers of nonexotic
quark-antiquark mesons at N_c = infinity and in the limit of t going to minus
infinity. In this region renormalization group improved perturbation theory
should be valid. We discuss the compatibility of nonlinear trajectories with
narrow resonance approximations.
|
hep-ph/9205211
| 727,326 |
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical
simulations of quantum field theories based on stochastic quantization and the
Langevin equation. The topics discussed include renormalization of finite
step-size algorithms, Fourier acceleration, and the relation of the Langevin
equation to hybrid stochastic algorithms and hybrid Monte Carlo.
|
hep-lat/9205008
| 727,326 |
We re-examine the gravitational wave background resulting from inflation and
its effect on the cosmic microwave background radiation. The new COBE
measurement of a cosmic background quadrupole anisotropy places an upper limit
on the vacuum energy during inflation of $\approx 5 \times 10^{16}$ GeV. A
stochastic background of gravitational waves from inflation could produce the
entire observed signal (consistent with the observed dipole anisotropy and a
flat spectrum) if the vacuum energy during inflation was as small as $1.5
\times 10^{16}$ GeV at the 95\% confidence level. This coincides nicely with
the mass scale for Grand Unification inferred from precision measurements of
the electroweak and strong coupling constants, for the SUSY Grand Unified
Theories. Thus COBE could be providing the first direct evidence, via
gravitational waves, for GUTs, and supersymmetry. Further tests of this
possibility are examined, based on analyzing the energy density associated with
gravitational waves from inflation.
|
hep-ph/9205212
| 727,326 |
Contents:
1. Quasiconformal Surgery and Deformations: Ben Bielefeld, Questions in
quasiconformal surgery; Curt McMullen, Rational maps and Teichm\"uller space;
John Milnor, Thurston's algorithm without critical finiteness; Mary Rees, A
possible approach to a complex renormalization problem.
2. Geometry of Julia Sets: Lennart Carleson, Geometry of Julia sets; John
Milnor, Problems on local connectivity.
3. Measurable Dynamics: Mikhail Lyubich, Measure and Dimension of Julia Sets;
Feliks Przytycki, On invariant measures for iterations of holomorphic maps.
4. Iterates of Entire Functions: Robert Devaney, Open questions in
non-rational complex dynamics; Alexandre Eremenko and Mikhail Lyubich,
Wandering domains for holomorphic maps.
5. Newton's Method: Scott Sutherland, Bad polynomials for Newton's method
|
math/9205209
| 727,327 |
A very weakly coupled scalar field with mass $m$ and initial vacuum
expectation value $V$ will provide enough mass to close the universe provided
$V\simeq (3\times 10^8\gev)(100\gev/m)^{1/4}$. We discuss possible models in
which such a field could arise.
|
astro-ph/9205005
| 727,327 |
The constraints imposed by asymptotic freedom and analyticity on the
large-order behavior of perturbation theory for the electromagnetic
current-current correlation function are examined. By suitably applying the
renormalization group, the coefficients of the asymptotic expansion in the deep
Euclidean region may be expressed explicitly in terms of the perturbative
coefficients of the Minkowski space discontinuity (the $R$-ratio in $e^+ e^-$
scattering). This relation yields a ``generic'' prediction for the large-order
behavior of the Euclidean perturbation series and suggests the presence of
non-perturbative $1/q^2$ correction in the Euclidian correlation function. No
such ``generic'' prediction can be made for the physically measurable
$R$-ratio. A novel functional method is developed to obtain these results.
|
hep-ph/9205213
| 727,327 |
We examine the application of $c=1$ conformal field theory to the description
of the fractional quantum Hall effect (FQHE). It is found that the Gaussian
model together with an appropriate boundary condition for the order parameter
furnishes an effective theory for the Laughlin type FQHE. The plateau formation
condition corresponds to taking the {\em chiral} portion of the theory.
|
hep-th/9205017
| 727,327 |
The oscillations of pseudo-Dirac neutrinos in matter are discussed and
applied to the solar neutrino problem. Several scenarios such as both $\nu_e$
and $\nu_{\mu}$ being pseudo-Dirac and only $\nu_e$ or $\nu_{\mu}$ being
pseudo-Dirac are examined. It is shown that the allowed region in the
mass-mixing angle parameter space obtained by comparing the solar neutrino data
with the calculations based on the standard solar model and the MSW effect is
not unique. The results depend on the nature of neutrinos; for example, if both
$\nu_e$ and $\nu_{\mu}$ are pseudo-Dirac, the allowed region determined by the
current solar neutrino data does not overlap with that obtained in the usual
case of pure Dirac or Majorana neutrinos.
|
hep-ph/9205214
| 727,327 |
The geometric interpretation of the antibracket formalism given by Witten is
extended to cover the anti-BRST symmetry. This enables one to formulate the
quantum master equation for the BRST--anti-BRST formalism in terms of
integration theory over a supermanifold. A proof of the equivalence of the
standard antibracket formalism with the antibracket formalism for the
BRST--anti-BRST symmetry is also given.
|
hep-th/9205018
| 727,327 |
We have performed Monte Carlo simulations of the Ising model coupled to
three-dimensional quantum gravity based on a summation over dynamical
triangulations. These were done both in the microcanonical ensemble, with the
number of points in the triangulation and the number of Ising spins fixed, and
in the grand canoncal ensemble. We have investigated the two possible cases of
the spins living on the vertices of the triangulation (``diect'' case) and the
spins living in the middle of the tetrahedra (``dual'' case). We observed phase
transitions which are probably second order, and found that the dual
implementation more effectively couples the spins to the quantum gravity.
|
hep-lat/9205009
| 727,327 |
String effective theories contain a dilaton scalar field which couples to
gravity, matter and radiation. In general, particle masses will have different
dilaton couplings. We can always choose a conformal frame in which baryons have
constant masses while (non--baryonic) dark matter have variable masses, in the
context of a scalar--tensor gravity theory. We are interested in the
phenomenology of this scenario. Dark matter with variable masses could have a
measurable effect on the dynamical motion of the halo of spiral galaxies, which
may affect cold dark matter models of galaxy formation. As a consequence of
variable masses, the energy--momentum tensor is not conserved; there is a
dissipative effect, due to the dilaton coupling, associated with a ``dark
entropy" production. In particular, if axions had variable masses they could be
diluted away, thus opening the ``axion window". Assuming that dark matter with
variable masses dominates the cosmological evolution during the matter era, it
will affect the primordial nucleosynthesis predictions on the abundances of
light elements. Furthermore, the dilaton also couples to radiation in the form
of a variable gauge coupling. Experimental bounds will constrain the parameters
of this model.
|
hep-ph/9205216
| 727,329 |
In view of the applications to the asymptotic analysis of a family of
obstacle problems, we consider a class of convex local functionals $F(u,A)$,
defined for all functions $u$ in a suitable vector valued Sobolev space and for
all open sets $A$ in ${\bf R}^n$. Sufficient conditions are given in order to
obtain an integral representation of the form $F(u,A)=\int_A f(x,u(x))\,d\mu +
\nu(A)$, where $\mu$ and $\nu$ are Borel measures and $f$ is convex in the
second variable.
|
funct-an/9205002
| 727,329 |
We analyze the statistical mechanics of a gas of neutral and charged black
holes. The microcanonical ensemble is the only possible approach to this
system, and the equilibrium configuration is the one for which most of the
energy is carried by a single black hole. Schwarzschild black holes are found
to obey the statistical bootstrap condition. In all cases, the microcanonical
temperature is identical to the Hawking temperature of the most massive black
hole in the gas. U(1) charges in general break the bootstrap property. The
problems of black hole decay and of quantum coherence are also addressed.
|
hep-th/9205021
| 727,329 |
In most attempts to compute the Hartle-Hawking ``wave function of the
universe'' in Euclidean quantum gravity, two important approximations are made:
the path integral is evaluated in a saddle point approximation, and only the
leading (least action) extremum is taken into account. In (2+1)-dimensional
gravity with a negative cosmological constant, the second assumption is shown
to lead to incorrect results: although the leading extremum gives the most
important single contribution to the path integral, topologically inequivalent
instantons with larger actions occur in great enough numbers to predominate.
One can thus say that in 2+1 dimensions --- and possibly in 3+1 dimensions as
well --- entropy dominates action in the gravitational path integral.
|
hep-th/9205022
| 727,329 |
We propose and investigate a large class of models possessing resonance
factorized S-matrices. The associated Casimir energy describes a rich pattern
of renormalization group trajectories related to flows in the coset models
based on the simply laced Lie Algebras. From a simplest resonance S-matrix,
satisfying the ``$\phi^3$-property'', we predict new flows in non-unitary
minimal models.
|
hep-th/9205024
| 727,330 |
We study the scattering of a massless and neutral test particle in the
gravitational field of a body (the string star) made of a large number of
scalar states of the superstring. We consider two cases, the one in which these
states are neutral string excitations massive already in ten dimensions and the
one in which their masses (and charges) originate in the process of
compactification on tori. A perturbative calculation based on superstring
amplitudes gives us the deflection angle up to the second order in Newton's
constant. A comparison with field theory explicitly shows which among the
various massless fields of the superstring give a contribution to the
scattering process. In both cases, the deflection angle is smaller than the one
computed in general relativity. The perturbative series can be resummed by
finding the exact solution to the classical equations of motion of the
corresponding low-energy action. The space-time metric of our two examples of
string stars has no horizon.
|
hep-th/9205025
| 727,330 |
Starting from a Poincar\'e invariant field theory of a real scalar field with
interactions governed by a double-well potential in 2+1 dimensions, the Lorentz
representation induced on the collective coordinates describing low-energy
excitations about an effective string background is derived. In this
representation, Lorentz transformations are given in terms of an infinite
series, in powers of derivatives along the worldsheet. Transformations that act
on the direction transverse to the string worldsheet involve a universal
dimension $-1$ term. As a consequence, Lorentz invariance holds in this theory
of long effective strings due to cancellations in the action between irrelevant
terms and the dimension two term that describes free massless scalar fields in
two dimensions. (in plain tex, no macropackages necessary)
|
hep-th/9205026
| 727,330 |
The group PGL(2) of linear transformations of the projective line acts
naturally on the d-dimensional projective space P^d parametrizing
configurations (`d-tuples') of points on the line. In this note we are
concerned with the orbits of this action of PGL(2) on P^d. The closure of each
orbit is a projective subvariety of P^d of which we determine the degree, the
`boundary'--i.e., the complement of an orbit in its closure--, and the
multiplicity at points of the boundary. These results are used to provide a
complete classification of the non-singular orbit closures, and criteria for an
orbit closure to be non-singular in codimension 1.
|
alg-geom/9205005
| 727,330 |
We investigate the stability of charged black holes in two-dimensional
heterotic string theories that were recently discussed by McGuidan, Nappi and
Yost. In the framework of small time-dependent perturbation, we find that these
black holes are linearly stable.
|
hep-th/9205023
| 727,330 |
In supersymmetric theories the mass of any state is bounded below by the
values of some of its charges. The corresponding bounds in case of
Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with
the requirement that naked singularities be absent. Here we investigate charged
dilaton black holes in this context. We show that the extreme solutions
saturate the supersymmetry bound of $N=4\ d=4$ supergravity, or dimensionally
reduced superstring theory. Specifically, we have shown that extreme dilaton
black holes, with electric and magnetic charges, admit super-covariantly
constant spinors. The supersymmetric positivity bound for dilaton black holes,
$M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked
singularities of the dilaton black holes and is, in this sense, equivalent to
the cosmic censorship condition. The temperature, entropy and singularity are
discussed. The Euclidean action (entropy) of the extreme black hole is given by
$2\pi |PQ|$. We argue that this result, as well as the one for Lorentzian
signature, is not altered by higher order corrections in the supersymmetric
theory. When a black hole reaches its extreme limit, it cannot continue to
evaporate by emitting elementary particles, since this would violate the
supersymmetric positivity bound. We speculate on the possibility that an
extreme black hole may ``evaporate" by emitting smaller extreme black holes.
|
hep-th/9205027
| 727,331 |
Recently Callan, Giddings, Harvey and the author derived a set of one-loop
semiclassical equations describing black hole formation/evaporation in
two-dimensional dilaton gravity conformally coupled to $N$ scalar fields. These
equations were subsequently used to show that an incoming matter wave develops
a black hole type singularity at a critical value $\phi_{cr}$ of the dilaton
field. In this paper a modification to these equations arising from the
Fadeev-Popov determinant is considered and shown to have dramatic effects for
$N<24$, in which case $\phi_{cr}$ becomes complex. The $N<24$ equations are
solved along the leading edge of an incoming matter shock wave and found to be
non-singular. The shock wave arrives at future null infinity in a zero energy
state, gravitationally cloaked by negative energy Hawking radiation. Static
black hole solutions supported by a radiation bath are also studied. The
interior of the event horizon is found to be non-singular and asymptotic to
deSitter space for $N<24$, at least for sufficiently small mass. It is noted
that the one-loop approximation is {\it not} justified by a small parameter for
small $N$. However an alternate theory (with different matter content) is found
for which the same equations arise to leading order in an adjustable small
parameter.
|
hep-th/9205028
| 727,331 |
We study the BRST quantization of the 1+1 dimensional gravity model proposed
by Jackiw and Teitelboim and also the topological gauge model which is
equivalent to the gravity model at least classically. The gravity model
quantized in the light-cone gauge is found to be a free theory with a nilpotent
BRST charge. We show also that there exist twisted N=2 superconformal algebras
in the Jackiw-Teitelboim's model as well as in the topological gauge model. We
discuss the quantum equivalence between the gravity theory and the topological
gauge theory. It is shown that these theories are indeed equivalent to each
other in the light-cone gauge.
|
hep-th/9205030
| 727,331 |
The quark-hadron phase transition in the early universe can produce
inhomogeneities in the distribution of nucleons, which in turn affect the
primordial nucleosynthesis. In all the investigations of this problem it has
been assumed that the degree of supercooling of the quark-gluon plasma after
the phase transition is large enough to produce a significant rate of
nucleation of hadrons. Using the latest results of finite temperature lattice
QCD and the finite size scaling theory, we argue that the degree of
supercooling is in fact extremely small and hence the nucleation rate is
negligible.
|
astro-ph/9205006
| 727,331 |
The addition of a topological model to the matter content of a conventional
closed-string theory leads to the appearance of many perturbatively-decoupled
space-time worlds. We illustrate this by classifying topological vertex models
on a triangulated surface. We comment on how such worlds could have been
coupled in the Planck era.
|
hep-th/9205031
| 727,331 |
Doncheski and Hewett have recently shown that the ratio of neutral current to
charged current cross sections, $R={\sigma_{NC}}/{\sigma_{CC}}$, can provide a
more sensitive probe for the existence of heavy leptoquarks at HERA than the
usual proceedure which makes use of neutral current asymmetries. The apparent
reason for this is that the Standard Model expectations for {\it both} of these
cross sections are modified by the existence of such particles in a
semi-coherent manner. In this paper we apply this technique to extended
electroweak models whose spectrum contains both a $W'$ and a $Z'$. We find that
measurements of $R$ can, for some models, substantially increase the HERA
search range for new gauge bosons beyond that which can be probed using the
more conventional asymmetries.
|
hep-ph/9205218
| 727,331 |
It is shown that the N=2 superconformal transformations are restricted N=1
supergauge transformations of a supergauge theory with Osp(2,2) as a gauge
group. Based on this result, a canonical derivation of the Osp(2,2) current
algebra in the superchiral gauge formulation of N=2 supergravity is presented.
|
hep-th/9205032
| 727,331 |
Neutrino decay in the minimal seesaw model containing three right handed
neutrinos and a complex $SU(2)\times U(1)$ singlet Higgs in addition to the
standard model fields is considered. A global horizontal symmetry $U(1)_H$ is
imposed, which on spontaneous breaking gives rise to a Goldstone boson. This
symmetry is chosen in a way that makes a) the contribution of heavy ($\leq$
MeV) majorana neutrinos to the neutrinoless double beta decay amplitude
vanish and b) allows the heavy neutrino to decay to a lighter neutrino and the
Goldstone boson. It is shown that this decay can occur at a rate much faster
than in the original Majoron model even if one does not introduce any
additional Higgs fields as is done in the literature. Possibility of describing
the 17 keV neutrino in this minimal seesaw model is investigated. While most of
the cosmological and astrophysical constraints on the 17 keV neutrino can be
satisfied in this model, the laboratory limits coming from the neutrino
oscillations cannot be easily met. An extension which removes this inadequacy
and offers a consistent description of the 17 keV neutrino is discussed.
|
hep-ph/9205220
| 727,331 |
The three-point functions for minimal models coupled to gravity are derived
in the operator approach to Liouville theory which is based on its $U_q(sl(2))$
quantum group structure. The result is shown to agree with matrix-model
calculations on the sphere. The precise definition of the corresponding
cosmological constant is given in the operator solution of the quantum
Liouville theory. It is shown that the symmetry between quantum-group spins $J$
and $-J-1$ previously put forward by the author is the explanation of the
continuation in the number of screening operators discovered by Goulian and Li.
Contrary to the previous discussions of this problem, the present approach
clearly separates the emission operators for each leg. This clarifies the
structure of the dressing by gravity. It is shown, in particular that the end
points are not treated on the same footing as the mid point. Since the outcome
is completely symmetric this suggests the existence of a picture-changing
mechanism in two dimensional gravity.
|
hep-th/9205034
| 727,331 |
The Euclidean analogues of the sine-Gordon solitons are used as sources of
the heterotic fivebrane solutions in the ten-dimensional heterotic string
theory. Some properties of these soliton solutions are discussed. These
solitons in principle can appear as string-like objects in 4-dimensional
space-time after proper compactifications.
|
hep-th/9205035
| 727,331 |
Necessary and sufficient conditions are found for any object in $3+1$
dimensions to have integer rather than fractional fermion number. Nontrivial
examples include the Jackiw-Rebbi monopole and the already well studied
Su-Schrieffer-Heeger soliton, both displaying integer multiples of elementary
charges in combinations that normally are forbidden.
|
hep-th/9205036
| 727,331 |
We present a global analysis of the geometries that arise in non-compact
current algebra (or gauged WZW) coset models of strings and particles
propagating in curved space-time. The simplest case is the 2d black hole. In
higher dimensions these geometries describe new and much more complex
singularities. For string and particle theories (defined in the text) we
introduce general methods for identifying global coordinates and give the
general exact solution for the geodesics for any gauged WZW model for any
number of dimensions. We then specialize to the 3d geometries associated with
$SO(2,2)/SO(2,1)$ (and also $SO(3,1)/SO(2,1)$) and discuss in detail the global
space, geodesics, curvature singularities and duality properties of this space.
The large-small (or mirror) type duality property is reformulated as an
inversion in group parameter space. The 3d global space has two topologically
distinct sectors, with patches of different sectors related by duality. The
first sector has a singularity surface with the topology of ``pinched double
trousers". It can be pictured as the world sheet of two closed strings that
join into a single closed string and then split into two closed strings, but
with a pinch in each leg of the trousers. The second sector has a singularity
surface with the topology of ``double saddle", pictured as the world sheets of
two infinite open strings that come close but do not touch. We discuss the
geodesicaly complete spaces on each side of these surfaces and interpret the
motion of particles in physical terms. A cosmological interpretation is
suggested and comments are mode on possible physical applications.
|
hep-th/9205037
| 727,331 |
The second order correction to free energy due to the interaction between
electrons is calculated for a quasi-one-dimensional conductor exposed to a
magnetic field perpendicular to the chains. It is found that specific heat,
magnetization and torque oscillate when the magnetic field is rotated in the
plane perpendicular to the chains or when the magnitude of magnetic filed is
changed. This new mechanism of thermodynamic magnetic oscillations in metals,
which is not related to the presence of any closed electron orbits, is applied
to explain behavior of the organic conductor (TMTSF)$_2$ClO$_4$.
|
cond-mat/9205007
| 727,332 |
Parquet equations, describing the competition between superconducting and
density-wave instabilities, are solved for a three-dimensional isotropic metal
in a high magnetic field when only the lowest Landau level is filled. In the
case of a repulsive interaction between electrons, a phase transition to the
density-wave state is found at finite temperature. In the opposite case of
attractive interaction, no phase transition is found. With decreasing
temperature $T$, the effective vertex of interaction between electrons
renormalizes toward a one-dimensional limit in a self-similar way with the
characteristic length (transverse to the magnetic field) decreasing as
$\ln^{-1/6}(\omega_c/T)$ ($\omega_c$ is a cutoff). Correlation functions have
new forms, previously unknown for conventional one-dimensional or
three-dimensional Fermi-liquids.
|
cond-mat/9205008
| 727,332 |
To the Yang-Baxter equation an additional relation can be added. This is the
reflection equation which appears in various places, with or without spectral
parameter. For example, in factorizable scattering on a half-line, integrable
lattice models with non-periodic boundary conditions, non-commutative
differential geometry on quantum groups, etc. We study two forms of spectral
parameter independent reflection equations, chosen by the requirement that
their solutions be comodules with respect to the quantum group coaction leaving
invariant the reflection equations. For a variety of known solutions of the
Yang-Baxter equation we give the constant solutions of the reflection
equations. Various quadratic algebras defined by the reflection equations are
also given explicitly.
|
hep-th/9205039
| 727,332 |
From an accurate determination of the inter-quark potential, one can study
the running coupling constant for a range of $R$-values and hence estimate the
scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(2)$ pure
gauge theory to illustrate the method.
|
hep-lat/9205010
| 727,332 |
The partition functions of Pasquier models on the cylinder, and the
associated intertwiners, are considered. It is shown that earlier results due
to Saleur and Bauer can be rephrased in a geometrical way, reminiscent of
formulae found in certain purely elastic scattering theories. This establishes
the positivity of these intertwiners in a general way and elucidates
connections between these objects and the finite subgroups of SU(2). It also
offers the hope that analogous geometrical structures might lie behind the
so-far mysterious results found by Di Francesco and Zuber in their search for
generalisations of these models.
|
hep-th/9205040
| 727,332 |
We consider Calabi-Yau compactifications with one K\"ahler modulus. Following
the method of Candelas et al. we use the mirror hypothesis to solve the quantum
theory exactly in dependence of this modulus by performing the calculation for
the corresponding complex structure deformation on the mirror manifold. Here
the information is accessible by techniques of classical geometry. It is
encoded in the Picard-Fuchs differential equation which has to be supplemented
by requirements on the global properties of its solutions.
|
hep-th/9205041
| 727,332 |
A reorganized perturbation expansion with a propagator of soft infrared
behavior is used to study the critical behavior of the mass gap. The condition
of relativistic covariance fixes the form of the soft propagator. Finite
approximants to the correlation critical exponent can be obtained in every
order of the modified, soft perturbation expansion. Alternatively, a convergent
series of exponents in large orders of the soft perturbation expansion is
provided by the renormalization group in all spatial dimensions, $1\leq
D\leq3$. The result of the $\epsilon$-expansion is recovered in the
$D\rightarrow 3 $ limit.
|
hep-th/9205042
| 727,332 |
For g < f in omega^omega we define c(f,g) be the least number of uniform
trees with g-splitting needed to cover a uniform tree with f-splitting. We show
that we can simultaneously force aleph_1 many different values for different
functions (f,g). In the language of Blass: There may be aleph_1 many distinct
uniform Pi^0_1 characteristics.
|
math/9205208
| 727,333 |
We discuss nonfactorizable $1/N_c$ contributions in the amplitudes of
non-leptonic exclusive decays of the type $B\rightarrow D\pi$ ($N_c$ is the
number of colors). In a certain kinematical limit rather reliable estimates are
possible. It is demonstrated that the nonfactorizable parts are of the same
order as the factorizable $1/N_c$ parts of the ampiltudes, and have the
opposite sign. Thus, an approximate rule of discarding $1/N_c$ corrections in
the nonleptonic exclusive decays emerges dynamically. It is shown that this
rule is not exact and the degree of compensation is different in different
channels.
Our predictions make use of the fact that a key matrix element that measures
deviations from factorization can be determined using the heavy quark effective
theory.
|
hep-ph/9205221
| 727,333 |
We find that the high temperature limit of the free energy per unit length
for the rigid string agrees dimensionally with that of the QCD string (unlike
the Nambu-Goto string). The sign, and in fact the phase, do not agree. While
this may be a clue to a string theory of QCD, we note that the problem of the
fourth derivative action makes it impossible for the rigid string to be a
correct description.
|
hep-th/9205043
| 727,333 |
The quantum Hamiltonian reduction on the OSp(1,2) super Kac-Moody algebra is
described in the BRST formalism. Using a free field representation of the KM
currents, the super Kac-Moody algebra is shown to be reduced to a
superconformal one via the Hamiltonian reduction. This reduction is manifestly
supersymmetric because of supersymmetric constraints imposed on the algebra.
|
hep-th/9205044
| 727,333 |
The new contributions to the electron (muon) anomalous magnetic moment
arising in mirror fermion theories have been calculated. Imposing the
experimental constraint lowers the current upper bound on the ordinary - mirror
lepton mixing angles by a factor of 50 making predictions for mirror lepton
production at HERA undetectably small. A way out is to allow for different
mixing angles of the L and R field components. Choosing very small right mixing
angles compatibility with the anomalous magnetic moment measurement may be
easily maintained, while choosing left mixing angles close to the upper limits
yields still reasonable HERA cross-sections.
|
hep-ph/9205222
| 727,333 |
We study the two-dimensional supersymmetric Toda theory based on the Lie
superalgebra $B(1,1) \equiv Osp(3|2)$ and construct its quantum W-currents. We
also investigate the fermionic affinization of this model: we show that despite
the non-unitary form of the Lagrangian the $B^{(1)}(1,1)$ theory has a real
particle mass spectrum which is not renormalized at one-loop. We construct the
first higher--spin conserved current, prove its conservation to all-loop order,
compute one-loop corrections to the corresponding charge and check consistency
between charge and mass renormalization.
|
hep-th/9205045
| 727,333 |
Spontaneous compactification ---on a $R^1\times S^1$ background--- in 2D
induced quantum gravity (considered as a toy model for more fundamental quantum
gravity) is analyzed in the gauge-independent effective action formalism. It is
shown that such compactification is stable, in contradistinction to
multidimensional quantum gravity on a $R^D\times S^1 \ (D>2)$ background
---which is known to be one-loop unstable.
|
hep-th/9205049
| 727,333 |
Renormalization group equations for massless GUT's in curved space-time with
non-trivial topology are formulated. The asymptotics of the effective action
both at high and low energies are obtained. It is shown that the Casimir energy
contribution at high curvature (early Universe) becomes non-essential in the
effective action.
|
hep-th/9205047
| 727,333 |
The calculation of the effective potential for fixed-end and toroidal rigid
$p$-branes is performed in the one-loop as well as in the $1/d$ approximations.
The analysis of the involved zeta-functions (of inhomogeneous Epstein type)
which appear in the process of regularization is done in full detail.
Assymptotic formulas (allowing only for exponentially decreasing errors of
order $\leq 10^{-3}$) are found which carry all the dependences on the basic
parameters of the theory explicitly. The behaviour of the effective potential
(specified to the membrane case $p=2$) is investigated, and the extrema of this
effective potential are obtained.
|
hep-th/9205050
| 727,333 |
The path integral for higher-derivative quantum gravity with torsion is
considered. Applying the methods of two-dimensional quantum gravity, this path
integral is analyzed in the limit of conformally self-dual metrics. A scaling
law for fixed-volume geometry is obtained.
|
hep-th/9205048
| 727,333 |
An action for two dimensional gravity conformally coupled to two dilaton-type
fields is analysed. Classically, the theory has some exact solutions. These
include configurations representing black holes. A semi-classical theory is
obtained by assuming that these singular solutions are caused by the collapse
of some matter fields. The semi-classical equations of motion reveal then that
any generic solution must have a flat geometry.
|
hep-th/9205053
| 727,333 |
We construct $N=2$ super-$W_{n+1}$ strings and obtain the complete physical
spectrum, for arbitrary $n \ge 2$. We also derive more general realisations of
the super-$W_{n+1}$ algebras in terms of $k$ commuting $N=2$ super
energy-momentum tensors and $n-k$ pairs of complex superfields, with $0\le k
\le [\ft{n+1}{2}]$.
|
hep-th/9205054
| 727,333 |
The string equation for the $[{\tilde P},Q]=Q$ formulation of
non--perturbatively stable 2D quantum gravity coupled to the $(2m-1,2)$ models
is studied. Global KdV flows between the appropriate solutions are considered
as deformations of two compatible linear problems. It is demonstrated that the
necessary conditions for such flows to exist are satisfied. A numerical study
reveals such flows between the pole--free solutions of pure gravity ($m=2$),
the Lee--Yang edge model ($m=3$) and topological gravity ($m=1$). We conjecture
that this is the case for all of the $m$--critical models. As the $m=1$
solution is unique these global flows define a {\sl unique} solution for each
$m$--critical model.
|
hep-th/9205056
| 727,334 |
We discuss a new method of integration over matrix variables based on a
suitable gauge choice in which the angular variables decouple from the
eigenvalues at least for a class of two-matrix models. The calculation of
correlation functions involving angular variables is simple in this gauge.
Where the method is applicable it also gives an extremely simple proof of the
classical integration formula used to reduce multi-matrix models to an integral
over the eigenvalues.
|
hep-th/9205057
| 727,336 |
We propose $\theta$ bag through the wall separating $\theta=0$ and
$\theta=\pi$. $\theta$ may or may not be a dynamical field generating the wall.
For a massive pseudo scalar $\theta$, we present a two Higgs doublet model. We
also presnt an idea for quark confinement within this $\theta$ bag scheme.
|
hep-ph/9205223
| 727,336 |
The open string with one-dimensional target space is formulated in terms of
an SOS, or loop gas, model on a random surface. We solve an integral equation
for the loop amplitude with Dirichlet and Neumann boundary conditions imposed
on different pieces of its boundary. The result is used to calculate the mean
values of order and disorder operators, to construct the string propagator and
find its spectrum of excitations. The latter is not sensible neither to the
string tension $\L$ nor to the mass $\mu$ of the ``quarks'' at the ends of the
string. As in the case of closed strings, the SOS formulation allows to
construct a Feynman diagram technique for the string interaction amplitudes.
|
hep-th/9205059
| 727,336 |
Gauge invariant chiral theories satisfying the reflection positivity is
constructed on a lattice. This requires the introduction of "half gauge fields"
defined some time ago by Brydges, Fr\"{o}hlich, and Seiler \cite{BFS}. A
two-dimensional model is considered in some detail.
|
hep-lat/9205012
| 727,336 |
An exact conformal field theory describing a four dimensional singular string
background is obtained by chiral gauging a $U(1)$ subgroup along with
translations in $R$ of an $SL(2,R)\times R$ Wess-Zumino-Witten model. It is
shown that the target space-time describes a four dimensional black membrane.
Furthermore various duality transformed solutions are constructed. These are
also shown to correspond to various forms of four dimensional black membranes.
|
hep-th/9205062
| 727,336 |
We describe the quantum mechanical scattering of slowly moving maximally
charged black holes. Our technique is to develop a canonical quantization
procedure on the parameter space of possible static classical solutions. With
this, we compute the capture cross sections for the scattering of two black
holes. Finally, we discuss how quantization on this parameter space relates to
quantization of the degrees of freedom of the gravitational field.
|
hep-th/9205061
| 727,336 |
The energy splitting $E_{0a}$ in two and four dimensional Ising models is
measured in a cylindrical geometry on finite lattices. By comparing to exact
results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be
extracted very reliably from Monte Carlo calculations in practice. In four
dimensions we compare the measured $E_{0a}$ with two different theoretical
predictions on the finite size behavior of the energy splitting. We find that
our numerical data are in favor of the predictions based on the semiclassical
dilute instanton gas approximation.
|
hep-lat/9205011
| 727,336 |
This thesis is a study of two dimensional noncritical string theory. The main
tool which is used, is the matrix model. Introductions to both the Liouville
model and its matrix model formulation are included. In particular the special
states are discussed. Some calculations of partition functions on genus one
using field theory techniques are given. Nonperturbative issues and string
theory at finite radius are discussed. Zero momentum correlation functions are
calculated using the matrix model. One important result is a set of recursion
relations. The treatment is extended to nonzero momentum. The main result is a
clear identification of the special states. Some comments on the Wheeler de
Witt equation is given. The matrix model $W_{\infty}$ algebra is introduced.
This organizes the previous results. In particular, a simple derivation of the
genus zero tachyon correlation functions is given. The results are then
extended to higher genus. It is seen how a deformation of the algebra is
responsible for much of the higher genus structure. Some very explicit formulae
are derived. Then the Liouville and matrix model calculations are compared
followed by some general conclusions.
|
hep-th/9205063
| 727,336 |
Various aspects of recent works on affine quantum group symmetry of
integrable 2d quantum field theory are reviewed and further clarified. A
geometrical meaning is given to the quantum double, and other properties of
quantum groups. Multiplicative presentations of the Yangian double are
analyzed.
|
hep-th/9205064
| 727,336 |
We propose a new construction of Banach-Lie groups and algebras relying on
nonstandard analysis. A major standard application is the Local Theorem which
to certain extent reduces the problem of associating a Lie group to a given
banach-Lie algebra to a similar problem for finitely generated Lie subalgebras.
We discuss possible applications, e.g., to gauge theories.
|
funct-an/9205003
| 727,337 |
Remarks are given to the structure of physical states in 2D gravity coupled
to $C\leq 1$ matter. The operator algebra of the discrete state operators is
calculated for the theory with non-vanishing cosmological constant.
|
hep-th/9205065
| 727,337 |
A kind of topological field theory is proposed as a candidate to describe the
global structure of the 2-form Einstein gravity with or without a cosmological
constant. Indeed in the former case, we show that a quantum state in the
candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST
quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried
out for this topological version of the 2-form Einstein gravity.
|
hep-th/9205066
| 727,337 |
Axions with variable masses, in the context of a scalar--tensor gravity
theory, give a large entropy production during the matter era. The subsequent
axion dilution is proportional to their present energy density. Depending on
the parameters ($\beta_I,\beta_V$) of the model, this dilution relaxes or even
eludes the cosmological bound on the axion mass, therefore opening the
so--called ``axion window".
|
hep-ph/9205224
| 727,337 |
From a Macaulay's paper it follows that a lex-segment ideal has the greatest
number of generators (the 0-th Betti number $\b_0$) among all the homogeneous
ideals with the same Hilbert function. In this paper we prove that this fact
extends to every Betti number, in the sense that all the Betti numbers of a
minimal free resolution of a lex segment ideal are bigger than or equal to the
ones of any homogeneous ideal with the same Hilbert function.
|
alg-geom/9205006
| 727,337 |
Effective field theories encode the predictions of a quantum field theory at
low energy. The effective theory has a fairly low ultraviolet cutoff. As a
result, loop corrections are small, at least if the effective action contains a
term which is quadratic in the fields, and physical predictions can be read
straight from the effective Lagrangean.
Methods will be discussed how to compute an effective low energy action from
a given fundamental action, either analytically or numerically, or by a
combination of both methods. Basically,the idea is to integrate out the high
frequency components of fields. This requires the choice of a "blockspin",i.e.
the specification of a low frequency field as a function of the fundamental
fields. These blockspins will be the fields of the effective field theory. The
blockspin need not be a field of the same type as one of the fundamental
fields, and it may be composite. Special features of blockspins in nonabelian
gauge theories will be discussed in some detail.
In analytical work and in multigrid updating schemes one needs interpolation
kernels $\A$ from coarse to fine grid in addition to the averaging kernels $C$
which determines the blockspin. A neural net strategy for finding optimal
kernels is presented.
Numerical methods are applicable to obtain actions of effective theories on
lattices of finite volume. The constraint effective potential) is of particular
interest. In a Higgs model it yields the free energy, considered as a function
of a gauge covariant magnetization. Its shape determines the phase structure of
the theory. Its loop expansion with and without gauge fields can be used to
determine finite size corrections to numerical data.
|
hep-lat/9205013
| 727,337 |
The original paper, as published in Nuclear Physics B in 1988, had a few
factor-of-two errors. Some people got confused by those errors. The purpose of
these errata is to make things clear. The revised version of the complete
article is also posted to hep-th.
|
hep-th/9205068
| 727,337 |
Like grand unification of old, string unification predicts simple tree-level
relations between the couplings of all unbroken gauge groups such as $SU(3)_C$
or $SU(2)_W\)$. I show here how to compute one-loop corrections to these
relations for any four-dimensional model based on a classical vacuum of the
heterotic string. The result can be used to calculate both $\sin^2\theta_W$ and
$\Lambda_{\rm QCD}$ in terms of $\alpha_{\rm QED}$ and $\mpl\)$.
The original version of this paper was written in 1987 and published in
Nuclear Physics in 1988. That version had a few factor-of-two errors, which
lead some people into confusion. To avoid future confusion, I've written
Errata; they are submitted separately to hep-th (article #9205068). This
submission is the complete revised version of the paper.
|
hep-th/9205070
| 727,337 |
We apply the solution for the strong CP-problem in the 4-dimensional
superstring theory recently proposed by Ib${\rm\acute{a}\tilde{n}}$ez and
L${\rm\ddot{u}}$st to Calabi-Yau type models and study its phenomenological
aspects. In Calabi-Yau type models there seem to be phenomenologically
difficult problems in the axion decoupling from the neutral gauge currents and
the compatibility between the proton stability and the cosmological bound on
the axion. DFSZ type invisible axion mechanism which works without heavy extra
colored fields may be more promising than KSVZ axion in the viewpoint of proton
stability.
|
hep-ph/9205225
| 727,338 |
The integrability of $R^2$-gravity with torsion in two dimensions is traced
to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian
phase space. It may be interpreted as a quadratically deformed
$iso(2,1)$-algebra with the deformation consisting of the Casimir operators of
the undeformed algebra. The locally conserved quantity encountered in the
explicit solution is identified as an element of the centre of this algebra.
Specific contractions of the algebra are related to specific limits of the
explicit solutions of this model.
|
hep-th/9205071
| 727,338 |
Modular invariant conformal field theories with just one primary field and
central charge $c=24$ are considered. It has been shown previously that if the
chiral algebra of such a theory contains spin-1 currents, it is either the
Leech lattice CFT, or it contains a Kac-Moody sub-algebra with total central
charge 24. In this paper all meromorphic modular invariant combinations of the
allowed Kac-Moody combinations are obtained. The result suggests the existence
of 71 meromorphic $c=24$ theories, including the 41 that were already known.
|
hep-th/9205072
| 727,338 |
We show how the stochastic stabilization provides both the weak coupling
genus expansion and a strong coupling expansion of 2d quantum gravity. The
double scaling limit is described by a hamiltonian which is unbounded from
below, but which has a discrete spectrum.
|
hep-th/9205073
| 727,338 |
Recent developments in superstring phenomenology are summarized on a
non-technical level. (Talk presented at the XXVIIth Rencontre de Moriond on
Electroweak Interactions and Unified Theories.)
|
hep-ph/9205226
| 727,338 |
In these lectures the relations between symmetries, Lie algebras, Killing
vectors and Noether's theorem are reviewed. A generalisation of the basic ideas
to include velocity-dependend co-ordinate transformations naturally leads to
the concept of Killing tensors. Via their Poisson brackets these tensors
generate an {\em a priori} infinite-dimensional Lie algebra. The nature of such
infinite algebras is clarified using the example of flat space-time. Next the
formalism is extended to spinning space, which in addition to the standard real
co-ordinates is parametrized also by Grassmann-valued vector variables. The
equations for extremal trajectories (`geodesics') of these spaces describe the
pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve
for the motion of a pseudo-classical electron in Schwarzschild space-time.
|
hep-th/9205074
| 727,338 |
We have studied numerically the dynamics of a directed elastic string in a
two-dimensional array of quenched random impurities. The string is driven by a
constant transverse force and thermal fluctuations are neglected. There is a
transition from pinned to unpinned behavior at a critical value $F_T$ of the
driving force. At the transition the average string velocity scales with the
driving force. The scaling is equally well described by a power law $v_d\sim
(F-F_T)^\zeta$, with $\zeta=0.24\pm0.1$, or by a logarithm,
$v_d\sim1/\ln(F-F_T)$. The divergence of the velocity-velocity correlation
length at threshold is characterized by an exponent $\nu=1.05\pm0.1$.
|
cond-mat/9205010
| 727,338 |
The rounding of the charge density wave depinning transition by thermal noise
is examined. Hops by localized modes over small barriers trigger
``avalanches'', resulting in a creep velocity much larger than that expected
from comparing thermal energies with typical barriers. For a field equal to the
$T=0$ depinning field, the creep velocity is predicted to have a {\em
power-law} dependence on the temperature $T$; numerical computations confirm
this result. The predicted order of magnitude of the thermal rounding of the
depinning transition is consistent with rounding seen in experiment.
|
cond-mat/9205011
| 727,338 |
Models with dynamical supersymmetry breaking have the potential to solve many
of the naturalness problems of hidden sector supergravity models. We review the
argument that in a generic supergravity theory in which supersymmetry is {\it
dynamically} broken in the hidden sector, only tiny Majorana masses for
gauginos are generated. This situation is similar to that of theories with
continuous R-symmetries, for which Hall and Randall have suggested that gluino
masses could arise through mixings with an octet of chiral fields. We note that
in hidden sector models, such mixing can only occur if the auxiliary D field of
a $U(1)$ gauge field has an expectation value. This in turn gives rise to a
catastrophically large Fayet-Iliopoulos term for ordinary hypercharge. To solve
this problem it is necessary to unify hypercharge at least partially in a
non-Abelian group. We consider, also, some general issues in models with
continuous or discrete R symmetries, noting that it may be necessary to include
$SU(2)$ triplet fields, and that these are subject to various constraints. In
the course of these discussions, we consider a number of naturalness problems.
We suggest that the so-called ``$\mu$-problem" is not a problem, and point out
that in models in which the axion decay constant is directly related to the
SUSY breaking scale, squarks, sleptons and Higgs particles generically acquire
huge masses.
|
hep-ph/9205227
| 727,338 |
The discrete model of the real symmetric one-matrix ensemble is analyzed with
a cubic interaction. The partition function is found to satisfy a recursion
relation that solves the model. The double-scaling limit of the recursion
relation leads to a Miura transformation relating the contributions to the free
energy coming from oriented and unoriented random surfaces. This transformation
is the same kind as found with a cuartic interaction.
|
hep-th/9205076
| 727,338 |
We apply elementary canonical methods for the quantization of 2+1 dimensional
gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons
action. As in a previous work, our approach does not involve choice of gauge or
clever manipulations of functional integrals. Instead, we just require the
Gauss law constraint for gravity to be first class and also to be everywhere
differentiable. When the spatial slice is a disc, the gravitational fields can
either be unconstrained or constrained at the boundary of the disc. The
unconstrained fields correspond to edge currents which carry a representation
of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an
algebra have been found using the method of induced representations. In the
case of constrained fields, we can classify all possible boundary conditions.
For several different boundary conditions, the field content of the theory
reduces precisely to that of 1+1 dimensional gravity theories. We extend the
above formalism to include sources. The sources take into account self-
interactions. This is done by punching holes in the disc, and erecting an
$ISO(2,1)$ Kac-Moody algebra on the boundary of each hole. If the hole is
originally sourceless, a source can be created via the action of a vertex
operator $V$. We give an explicit expression for $V$. We shall show that when
acting
|
hep-th/9205077
| 727,338 |
The nonlinear sigma model for which the field takes its values in the coset
space $O(1,2)/O(2)\times Z_2$ is similar to quantum gravity in being
perturbatively nonrenormalizable and having a noncompact curved configuration
space. It is therefore a good model for testing nonperturbative methods that
may be useful in quantum gravity, especially methods based on lattice field
theory. In this paper we develop the theoretical framework necessary for
recognizing and studying a consistent nonperturbative quantum field theory of
the $O(1,2)/O(2)\times Z_2$ model. We describe the action, the geometry of the
configuration space, the conserved Noether currents, and the current algebra,
and we construct a version of the Ward-Slavnov identity that makes it easy to
switch from a given field to a nonlinearly related one. Renormalization of the
model is defined via the effective action and via current algebra. The two
definitions are shown to be equivalent. In a companion paper we develop a
lattice formulation of the theory that is particularly well suited to the sigma
model, and we report the results of Monte Carlo simulations of this lattice
model. These simulations indicate that as the lattice cutoff is removed the
theory becomes that of a pair of massless free fields. Because the geometry and
symmetries of these fields differ from those of the original model we conclude
that a continuum limit of the $O(1,2)/O(2)\times Z_2$ model which preserves
these properties does not exist.
|
hep-lat/9205014
| 727,339 |
We review the current state of the homogeneous Banach space problem. We then
formulate several questions which arise naturally from this problem, some of
which seem to be fundamental but new. We give many examples defining the bounds
on the problem. We end with a simple construction showing that every infinite
dimensional Banach space contains a subspace on which weak properties have
become stable (under passing to further subspaces). Implications of this
construction are considered.
|
math/9205207
| 727,339 |
We calculate electric and magnetic form factors of protons and neutrons in
quenched Monte Carlo lattice QCD on a $16^3\times 24$ lattice at $\beta = 6.0$
using Wilson fermions. We employ a method which characterizes one of the
nucleon fields as a fixed zero-momentum secondary source. Extrapolating the
overall data set to the chiral limit, we find acceptable fits for either dipole
or monopole forms and extract proton and neutron magnetic moments, the
magnitude of which are $10$ to $15\%$ low compared to experiment. In the
extrapolation of the dipole fit of the form factors, we find that the dipole to
nucleon mass ratio is about $7\%$ low compared to experiment. In addition, we
obtain positive values of the neutron electric form factor, which, however, are
poorly represented by a popular phenomenological form at intermediate to small
$\kappa$ values. A zero-momentum technique for extracting hadron magnetic
moments is briefly discussed and shown to yield unrealistically small magnetic
moment values.
|
hep-lat/9205015
| 727,339 |
We present the first study of the light hadron spectrum and decay constants
for quenched QCD using an O(a)-improved nearest-neighbour Wilson fermion action
at \beta=6.2. We compare the results with those obtained using the standard
Wilson fermion action, on the same set of 18 gauge field configurations of a
24^3 times 48 lattice. For pseudoscalar meson masses in the range 330-800 MeV,
we find no significant difference between the results for the two actions. The
scales obtained from the string tension and mesonic sector are consistent, but
differ from that derived from baryon masses. The ratio of the pseudoscalar
decay constant to the vector meson mass is roughly independent of quark mass as
observed experimentally, and in approximate agreement with the measured value.
|
hep-lat/9205016
| 727,339 |
Since fields in the heavy quark effective theory are described by both a
velocity and a residual momentum, there is redundancy in the theory: small
shifts in velocity may be absorbed into a redefinition of the residual
momentum. We demonstrate that this trivial reparameterisation invariance has
non-trivial consequences: it relates coefficients of terms of different orders
in the $1/m$ expansion and requires linear combinations of these operators to
be multiplicatively renormalised. For example, the operator $-D^2/2m$ in the
effective lagrangian has zero anomalous dimension, coefficient one, and does
not receive any non-perturbative contributions from matching conditions. We
also demonstrate that this invariance severely restricts the forms of operators
which may appear in chiral lagrangians for heavy particles.
|
hep-ph/9205228
| 727,339 |
An exact conformal field theory describing a four dimensional 2-brane
solution is found by considering a chiral gauged Wess-Zumino -Witten theory
corresponding to $SL(2, R)\times R$ , where one gauges the one dimensional
$U(1)$ subgroup together with a translation in $R$. The backgrounds for string
propagation are explicitly obtained and the target space is shown to have a
true curvature singularity.
|
hep-th/9205078
| 727,339 |
The mass of the axino is computed in realistic supersymmetric extensions of
the standard model. It is found to be strongly model dependent and can be as
small as a few keV but also as large as the gravitino mass. Estimates of this
mass can only be believed once a careful analysis of the scalar potential has
been performed.
|
hep-ph/9205229
| 727,340 |
We find a remarkably simple relationship between the following two models of
the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic
model consisting of Zygmund class vector fields on the unit circle; (2) The
complex-analytic model comprising 1-parameter families of schlicht functions on
the exterior of the unit disc which allow quasiconformal extension. Indeed, the
Fourier coefficients of the vector field in (1) turn out to be essentially the
same as (the first variations of) the corresponding power series coefficients
in (2). These identities have many applications; in particular, to conformal
welding, to the almost complex structure of Teichm\"uller space, to study of
the Weil-Petersson metric, to variational formulas for period matrices, etc.
These utilities are explored.
|
alg-geom/9205007
| 727,340 |
We initiate a program to study the relationship between the target space, the
spectrum and the scattering amplitudes in string theory. We consider scattering
amplitudes following from string theory and quantum field theory on a curved
target space, which is taken to be the $SU(2)$ group manifold, with special
attention given to the duality between contributions from different channels.
We give a simple example of the equivalence between amplitudes coming from
string theory and quantum field theory, and compute the general form of a
four-scalar field theoretical amplitude. The corresponding string theory
calculation is performed for a special case, and we discuss how more general
string theory amplitudes could be evaluated.
|
hep-th/9205079
| 727,340 |
A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is
developed, based on the continuum theory presented in the preceding paper.
Special attention is given to choosing a lattice action (the ``geodesic''
action) that is appropriate for fields having noncompact curved configuration
spaces. A consistent continuum limit of the model exists only if the
renormalized scale constant $\beta_R$ vanishes for some value of the bare scale
constant~$\beta$. The geodesic action has a special form that allows direct
access to the small-$\beta$ limit. In this limit half of the degrees of freedom
can be integrated out exactly. The remaining degrees of freedom are those of a
compact model having a $\beta$-independent action which is noteworthy in being
unbounded from below yet yielding integrable averages. Both the exact action
and the $\beta$-independent action are used to obtain $\beta_R$ from Monte
Carlo computations of field-field averages (2-point functions) and
current-current averages. Many consistency cross-checks are performed. It is
found that there is no value of $\beta$ for which $\beta_R$ vanishes. This
means that as the lattice cutoff is removed the theory becomes that of a pair
of massless free fields. Because these fields have neither the geometry nor the
symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$
model has no continuum limit.
|
hep-lat/9205017
| 727,340 |
We propose a new global optimization method ({\em Simulated Tempering}) for
simulating effectively a system with a rough free energy landscape (i.e. many
coexisting states) at finite non-zero temperature. This method is related to
simulated annealing, but here the temperature becomes a dynamic variable, and
the system is always kept at equilibrium. We analyze the method on the Random
Field Ising Model, and we find a dramatic improvement over conventional
Metropolis and cluster methods. We analyze and discuss the conditions under
which the method has optimal performances.
|
hep-lat/9205018
| 727,340 |
An exact multimonopole solution of heterotic string theory is presented. The
solution is constructed by a modification of the 't Hooft ansatz for a
four-dimensional instanton. An analogous solution in Yang-Mills field theory
saturates a Bogomoln'yi bound and possesses the topology and far field limit of
a multimonopole configuration, but has divergent action near each source. In
the string solution, however, the divergences from the Yang-Mills sector are
precisely cancelled by those from the gravity sector. The resultant action is
finite and easily computed. The Manton metric on moduli space for the
scattering of two string monopoles is found to be flat to leading order in the
impact parameter, in agreement with the trivial scattering predicted by a test
monopole calculation.
|
hep-th/9205081
| 727,341 |
The behaviour of the chiral condensate in QCD is investigated by means of a
study of the distribution of the zeros of the partition function in the complex
quark mass plane. Simulations are performed at fixed temperature on three
different spatial volumes at $\beta=5.04$ and at $\beta=4.9$ and $\beta=5.2$ on
a $4^4$ lattice. Evidence is found for a chirally related transition at
non-zero quark mass in the intermediate coupling region for $\beta < 5.2 $ but
superimposed upon a smooth behaviour for the condensate. The critical mass at
which this transition is found is only weakly dependent on the spatial volume
and decreas with decreasing temperature.
|
hep-lat/9205019
| 727,341 |
A previously proposed two-step algorithm for calculating the expectation
values of Chern-Simons graphs fails to determine certain crucial signs. The
step which involves calculating tetrahedra by solving certain non- linear
equations is repaired by introducing additional linear equations. As a first
step towards a new algorithm for general graphs we find useful linear equations
for those special graphs which support knots and links. Using the improved set
of equations for tetrahedra we examine the symmetries between tetrahedra
generated by arbitrary simple currents. Along the way we uncover the classical
origin of simple-current charges. The improved skein relations also lead to
exact identities between planar tetrahedra in level $K$ $G(N)$ and level $N$
$G(K)$ CS theories, where $G(N)$ denotes a classical group. These results are
recast as identities for quantum $6j$-symbols and WZW braid matrices. We obtain
the transformation properties of arbitrary graphs and links under simple
current symmetries and rank-level duality. For links with knotted components
this requires precise control of the braid eigenvalue permutation signs, which
we obtain from plethysm and an explicit expression for the (multiplicity free)
signs, valid for all compact gauge groups and all fusion products.
|
hep-th/9205082
| 727,342 |
The interface tension between Z(N) vacua in a hot SU(N) gauge theory (without
dynamical fermions) is computed at next to leading order in weak coupling. The
Z(N) interface tension is related to the instanton of an effective action,
which includes both classical and quantum terms; a general technique for
treating consistently the saddle points of such effective actions is developed.
Loop integrals which arise in the calculation are evaluated by means of zeta
function techniques. As a byproduct, up to two loop order we find that the
stable vacuum is always equivalent to the trivial one, and so respects charge
conjugation symmetry.
|
hep-ph/9205231
| 727,342 |
We compute the leading and next--to--leading corrections to the finite
temperature scalar potential for a 3+1 dimensional $\phi^4$ theory using a
systematic $1/N$ expansion. Our approach automatically avoids problems
associated with infrared divergences in ordinary perturbation theory in
$\hbar$. The leading order result does not admit a first order phase
transition. The subleading result shows that the exact theory can admit at best
only a very weak first order phase transition. For $N=4$ and weak scalar
coupling we find that $T_1$, the temperature at which tunneling from the origin
may begin in the case of a first order transition, must be less than about 0.5
percent larger than $T_2$, the temperature at which the origin changes from
being a local minimum to being a local maximum. We compare our results to the
effective potential found from a sum of daisy graphs.
|
hep-ph/9205232
| 727,343 |
In view of the expectation that the solitonic sector of the lower dimensional
world may be originated from the solitonic sector of string theory, various
solitonic solutions are reduced from the heterotic fivebrane solutions in the
ten-dimensional heterotic string theory. These solitons in principle can appear
after proper compactifications, {\it e.g.} toroidal compactifications.
|
hep-th/9205083
| 727,343 |
I develop a diagrammatic method for calculating chiral logarithms in the
quenched approximation. While not rigorous, the method is based on physically
reasonable assumptions, which can be tested by numerical simulations. The main
results are that, at leading order in the chiral expansion, (a) there are no
chiral logarithms in quenched $f_\pi$, for $m_u=m_d$; (b) the chiral logarithms
in $B_K$ and related kaon B-parameters are, for $m_d=m_s$, the same in the
quenched approximation as in the full theory; (c) for $m_\pi$ and the
condensate, there are extra chiral logarithms due to loops containing the
$\eta'$, which lead to a peculiar non-analytic dependence of these quantities
on the bare quark mass. Following the work of Gasser and Leutwyler, I discuss
how there is a predictable finite volume dependence associated with each chiral
logarithm. I compare the resulting predictions with numerical results: for most
quantities the expected volume dependence is smaller than the errors, but for
$B_V$ and $B_A$ there is an observed dependence which is consistent with the
predictions.
|
hep-lat/9205020
| 727,343 |
In a previous paper we derived a relation between the operator product
coefficients and anomalous dimensions. We explore this relation in the
$(\phi^4)_4$ theory and compute the coefficient functions in the products of
$\phi^2$ and $\phi^4$ to first order in the parameter $\lambda$. The
calculation results in two-loop beta functions.
|
hep-th/9205084
| 727,343 |
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