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Dynamical symmetry breaking in three-dimensional QED with N fermion flavours
is considered at finite temperature, in the large $N$ approximation. Using an
approximate treatment of the Schwinger-Dyson equation for the fermion
self-energy, we find that chiral symmetry is restored above a certain critical
temperature which depends itself on $N$. We find that the ratio of the
zero-momentum zero-temperature fermion mass to the critical temperature has a
large value compared with four-fermion theories, as had been suggested in a
previous work with a momentum-independent self-energy. Evidence of a
temperature- dependent critical $N$ is shown to appear in this approximation.
The phase diagram for spontaneous mass generation in the theory is presented in
$T-N$ space.
|
hep-ph/9207246
| 727,399 |
States in the absolute (semi-relative) cohomology but not in the relative
cohomology are examined through the component decomposition of the string field
theory action for the 2-D string. It is found that they are auxiliary fields
without kinetic terms, but are important for instance in the master equation
for the Ward-Takahashi identities. The ghost structure is analyzed in the
Siegel gauge, but it is noted that the absolute (semi-relative) cohomology
states are lost.
|
hep-th/9207063
| 727,399 |
The simplest realizations of the new inflationary scenario typically give
rise to primordial density fluctuations which deviate logarithmically from the
scale free Harrison - Zeldovich spectrum. We consider a number of such examples
and, in each case we normalize the amplitude of the fluctuations with the
recent COBE measurement of the microwave background anisotropy. The predictions
for the bulk velocities as well as anisotropies on smaller (~1-2 degrees)
angular scales are compared with the Harrison-Zeldovich case. Deviations from
the latter range from a few to about 15 percent. We also estimate the redshift
beyond which the quasars would not be expected to be seen. The inflationary
quasar cutoff redshifts can vary by as much as 25\% from the Harrison-Zeldovich
case. We find that the inflationary scenario provides a good starting point for
a theory of large scale structure in the universe provided the dark matter is a
combination of cold plus (~10-30 \%) hot components.
|
hep-ph/9207247
| 727,399 |
We simulate the melting of a 71 A diameter cluster of Cu. At low temperatures
the crystal exhibits facets. With increasing temperatures the open facets
pre-melt, the melted regions coalesce into a liquid envelope containing a
crystalline nucleus, and the nucleus finally goes unstable to the supercooled
liquid. Using critical droplet theory and experimental data for Cu, we explain
the thermodynamics of the coexistence region. The width of the transition
scales as (Number of particles) to the power (-1/4).
|
cond-mat/9207023
| 727,399 |
We argue that the torus partition sum in $2d$ (super) gravity, which counts
physical states in the theory, is a decreasing function of the renormalization
group scale. As an application we chart the space of $(\hat c\leq1)$ $c\leq1$
models coupled to (super) gravity, confirming and extending ideas due to A.
Zamolodchikov, and discuss briefly string theory, where our results imply that
the number of degrees of freedom decreases with time.
|
hep-th/9207064
| 727,399 |
It is argued with the help of an illustrative model, that the inter--species
hierarchy among the fermion masses and the quark mixing angles can be
accommodated naturally in the standard model with (approximate) flavor
democracy provided there are four families of sequential quark--leptons with
all members of the fourth family having roughly equal masses. The special
problem of light neutrino masses (if any) and possible solutions are also
discussed.
|
hep-ph/9207248
| 727,399 |
By numerical simulations in {\it real time} we provide evidence in favour of
sphaleron like transitions in the hot, symmetric phase of the electroweak
theory. Earlier performed observations of a change in the Chern-Simons number
are supplemented with a measurement of the lowest eigenvalues of the
three-dimensional staggered fermion Dirac operator and observations of the
spatial extension of energy lumps associated with the transition. The
observations corroborate on the interpretation of the change in Chern-Simons
numbers as representing continuum physics, not lattice artifacts. By combining
the various observations it is possible to follow in considerable detail the
time-history of thermal fluctuations of the classical gauge-field
configurations responsible for the change in the Chern-Simons number.
|
hep-lat/9207020
| 727,399 |
The recently reported solar neutrino signal in the $^{71}$Ga GALLEX detector
adds a new dimension to the solar neutrino puzzle, complementing the previously
known signals in $^{37}$Cl and water-Cherenkov detectors. Possible explanations
for this new signal in terms of matter-enhanced neutrino oscillations (MSW
effect) are already awaiting in the literature. We point out here that
long-wavelength vacuum oscillations can furnish an alternative explanation of
all three signals simultaneously; such solutions give neutrino spectra with
distinctive energy dependence and seasonal time dependence. %This is a Revtex
file, which is Latex-based but depends upon inputting the %Revtex style files
distributed by APS/Physical Review. For more information, %contact Peggy
Sutherland at [email protected], phone (516) 349-7800 ext 674
|
hep-ph/9207257
| 727,399 |
We compute the zero frequency current noise numerically and in several limits
analytically for the coulomb blockade problem consisting of two tunnel
junctions connected in series. At low temperatures over a wide range of
voltages, capacitances, and resistances it is shown that the noise measures the
variance in the number of electrons in the region between the two tunnel
junctions. The average current, on the other hand, only measures the mean
number of electrons. Thus, the noise provides additional information about
transport in these devices which is not available from measuring the current
alone.
|
cond-mat/9207024
| 727,399 |
The non-minimal coupling of a scalar field is considered in the framework of
Ashtekar's new variables formulation of gravity. A first order action
functional for this system is derived in which the field variables are a tetrad
field, and an SL(2,C) connection, together with the scalar field. The tetrad
field and the SL(2,C) connection are related to the Ashtekar variables for the
vacuum case by a conformal transformation. A canonical analysis shows that for
this coupling the equations of Ashtekar's formulation of canonical gravity are
non-polynomial in the scalar field. (to be published in Phys. Rev. D)
|
gr-qc/9207001
| 727,399 |
Radiative corrections to electroweak parameters in technicolor theories may
be evaluated by one of two techniques: either one estimates spectral function
integrals using scaled QCD data, or one uses naive dimensional analysis with a
chiral Lagrangian. The former yields corrections to electroweak parameters
proportional to the number of flavors and the number of colors, while the
latter is proportional to the number of flavors squared and is independent of
the number of colors. We attempt to resolve this apparent contradiction by
showing that the spectrum of technicolor one obtains by scaling QCD data to
high energies is unlikely to resemble that of an actual technicolor theory. The
resonances are likely to be much lighter than naively supposed and the
radiative corrections to electroweak parameters may by much larger. We also
argue that much less is known about the spectrum and the radiative corrections
in technicolor than was previously believed.
|
hep-ph/9207249
| 727,399 |
Two different but tightly connected problems, $U(1)$ and strong CP violation
problems, are discussed in two different models which exhibit both asymptotic
freedom and confinement. One of them is the 3d Polyakov's model of compact QED
and the other is 4d gluodynamics. It is shown that although both these models
possess the long range interactions of the topological charges, only in the
former case physics does not depend on $\theta$; while the latter exhibits an
explicit $\theta$- dependence. The crucial difference is due to the
observation, that the pseudoparticles of 4d gluodynamics possess an aditional
quantum number, apart of the topological charge $Q$ .
|
hep-ph/9207250
| 727,400 |
An exploratory numerical study of the influence of heavy fermion doublets on
the mass of the Higgs boson is performed in the decoupling limit of a chiral
$\rm SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model with mirror fermions. The
behaviour of fermion and boson masses is investigated at infinite bare quartic
coupling on $4^3 \cdot 8$, $6^3 \cdot 12$ and $8^3 \cdot 16$ lattices. A first
estimate of the upper bound on the renormalized quartic coupling as a function
of the renormalized Yukawa-coupling is given.
|
hep-lat/9207021
| 727,400 |
We investigate the crossover between weak and strong self-avoidance in a
simulation of random surfaces with extrinsic curvature. We consider both
dynamically triangulated and rigid surfaces with the two possible
discretizations of the extrinsic curvature term.
|
hep-lat/9207022
| 727,400 |
In this paper we show that every sequence (F_n) of finite dimensional
subspaces of a real or complex Banach space with increasing dimensions can be
``refined'' to yield an F.D.D. (G_n), still having increasing dimensions, so
that either every bounded sequence (x_n), with x_n in G_n for n in N, is weakly
null, or every normalized sequence (x_n), with x_n in G_n for n in N, is
equivalent to the unit vector basis of l_1.
Crucial to the proof are two stabilization results concerning Lipschitz
functions on finite dimensional normed spaces. These results also lead to other
applications. We show, for example, that every infinite dimensional Banach
space X contains an F.D.D. (F_n), with lim_{n to infty} dim (F_n)=infty, so
that all normalized sequences (x_n), with x_n in F_n, n in N, have the same
spreading model over X. This spreading model must necessarily be
1-unconditional over X.
|
math/9207207
| 727,400 |
We prove that if X is an infinite dimensional Banach lattice with a weak unit
then there exists a probability space (Omega, Sigma,mu) so that the unit sphere
S(L_1(Omega, Sigma, mu) is uniformly homeomorphic to the unit sphere S(X) if
and only if X does not contain l_{infty}^n's uniformly.
|
math/9207208
| 727,400 |
We study $I=3/2$ elastic $K\pi $ scattering to Born order using
nonrelativistic quark wavefunctions in a constituent-exchange model. This
channel is ideal for the study of nonresonant meson-meson scattering amplitudes
since s-channel resonances do not contribute significantly. Standard quark
model parameters yield good agreement with the measured S- and P-wave phase
shifts and with PCAC calculations of the scattering length. The P-wave phase
shift is especially interesting because it is nonzero solely due to $SU(3)_f$
symmetry breaking effects, and is found to be in good agreement with experiment
given conventional values for the strange and nonstrange constituent quark
masses.
|
hep-ph/9207251
| 727,400 |
We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass
model within the recently introduced multicanonical ensemble. Replica on
lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate
is found, we are able to give a lower bound on the number of statistically
independent groundstates sampled. Temperature dependence of the energy, entropy
and other quantities of interest are easily calculable. In particular we report
the groundstate results. Computations involving the spin glass order parameter
are more tedious. Our data indicate that the large $L$ increase of the
ergodicity time is reduced to an approximately $V^3$ power law. Altogether the
results suggest that the multicanonical ensemble improves the situation of
simulations for spin glasses and other systems which have to cope with similar
problems of conflicting constraints.
|
hep-lat/9207023
| 727,400 |
We construct the BRST operator for non-critical $W_3$-strings and discuss the
tachyon-like spectrum. For $N$-punctured spheres with $N \leq 5$ we briefly
describe a formal definition of the integral over $W_3$-moduli space.
|
hep-th/9207067
| 727,400 |
The recent 71Ga solar neutrino observation is combined with the 37Cl and
Kamiokande-II observations in an analysis for neutrino masses and mixings. The
allowed parameter region is found for matter enhanced mixings among all three
neutrino flavors. Distortions of the solar neutrino spectrum unique to three
flavors are possible and may be observed in continuing and next generation
experiments.
|
hep-ph/9208241
| 727,400 |
We propose the factorizable S-matrices of the massive excitations of the
non-unitary minimal model $M_{2,11}$ perturbed by the operator $\Phi_{1,4}$.
The massive excitations and the whole set of two particle S-matrices of the
theory is simply related to the $E_8$ unitary minimal scattering theory. The
counting argument and the Thermodynamic Bethe Ansatz (TBA) are applied to this
scattering theory in order to support this interpretation. Generalizing this
result, we describe a new family of NON UNITARY and DIAGONAL $ADE$-related
scattering theories. A further generalization suggests the magnonic TBA for a
large class of non-unitary $\G\otimes\G/\G$ coset models
($\G=A_{odd},D_n,E_{6,7,8}$) perturbed by $\Phi_{id,id,adj}$, described by
non-diagonal S-matrices.
|
hep-th/9207069
| 727,400 |
In the derivation of a pure spin connection action functional for gravity two
methods have been proposed. The first starts from a first order lagrangian
formulation, the second from a hamiltonian formulation. In this note we show
that they lead to identical results for the specific cases of pure gravity with
or without a cosmological constant.
|
gr-qc/9207002
| 727,400 |
Generalizing the Knizhnik-Zamolodchikov equations, we derive a hierarchy of
non-linear Ward identities for affine-Virasoro correlators. The hierarchy
follows from null states of the Knizhnik-Zamolodchikov type and the assumption
of factorization, whose consistency we verify at an abstract level. Solution of
the equations requires concrete factorization ans\"atze, which may vary over
affine-Virasoro space. As a first example, we solve the non-linear equations
for the coset constructions, using a matrix factorization. The resulting coset
correlators satisfy first-order linear partial differential equations whose
solutions are the coset blocks defined by Douglas.
|
hep-th/9207071
| 727,401 |
In this paper we consider extensions of the super Virasoro algebra by one and
two super primary fields. Using a non-explicitly covariant approach we compute
all SW-algebras with one generator of dimension up to 7 in addition to the
super Virasoro field. In complete analogy to W-algebras with two generators
most results can be classified using the representation theory of the super
Virasoro algebra. Furthermore, we find that the SW(3/2, 11/2)-algebra can be
realized as a subalgebra of SW(3/2, 5/2) at c = 10/7. We also construct some
new SW-algebras with three generators, namely SW(3/2, 3/2, 5/2), SW(3/2, 2, 2)
and SW(3/2, 2, 5/2).
|
hep-th/9207072
| 727,401 |
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of
$R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$
matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show
that quantum deformation of nonsimple superalgebra $su(n\mid n)$ requires its
extension to $u(n\mid n)$.
|
hep-th/9207075
| 727,401 |
We investigate the prospects for neutralino dark matter within the
Supersymmetric Standard Model (SSM) including the constraints from universal
soft supersymmetry breaking and radiative breaking of the electroweak symmetry.
The latter is enforced by using the one-loop Higgs effective potential which
automatically gives the one-loop corrected Higgs boson masses. We perform an
exhaustive search of the allowed five-dimensional parameter space and find that
the neutralino relic abundance $\Omega_\chi h^2_0$ depends most strongly on the
ratio $\xi_0\equiv m_0/m_{1/2}$. For $\xi_0\gg1$ the relic abundance is almost
always much too large, whereas for $\xi_0\ll1$ the opposite occurs. For
$\xi_0\sim1$ there are wide ranges of the remaining parameters for which
$\Omega_\chi\sim1$. We also determine that $m_{\tilde q}\gsim250\GeV$ and
$m_{\tilde l}\gsim100\GeV$ are necessary in order to possibly achieve
$\Omega_\chi\sim1$. These lower bounds are much weaker than the corresponding
ones derived previously when radiative breaking was {\it not} enforced.
|
hep-ph/9207253
| 727,401 |
We examine solitons in theories with heavy fermions. These ``quantum''
solitons differ dramatically from semi-classical (perturbative) solitons
because fermion loop effects are important when the Yukawa coupling is strong.
We focus on kinks in a $(1+1)$--dimensional $\phi^4$ theory coupled to
fermions; a large-$N$ expansion is employed to treat the Yukawa coupling $g$
nonperturbatively. A local expression for the fermion vacuum energy is derived
using the WKB approximation for the Dirac eigenvalues. We find that fermion
loop corrections increase the energy of the kink and (for large $g$) decrease
its size. For large $g$, the energy of the quantum kink is proportional to $g$,
and its size scales as $1/g$, unlike the classical kink; we argue that these
features are generic to quantum solitons in theories with strong Yukawa
couplings. We also discuss the possible instability of fermions to solitons.
|
hep-th/9207074
| 727,401 |
We report on a study of hadron thermodynamics with two flavors of Wilson
quarks on 12^3x6 lattices. We have studied the crossover between the high and
low temperature regimes for three values of the hopping parameter, kappa=0.16,
0.17, and 0.18. At each of these values of kappa we have carried out spectrum
calculations on 12^3x24 lattices for two values of the gauge coupling in the
vicinity of the crossover in order to set an energy scale for our
thermodynamics calculations and to determine the critical value of the gauge
coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we
find coexistence between the high and low temperature regimes over 1,000
simulation time units indicating either that the equilibration time is
extremely long or that there is a possibility of a first order phase
transition. The pion mass is large at the crossover values of the gauge
coupling, but the crossover curve has moved closer to the critical curve along
which the pion and quark masses vanish, than it was on lattices with four time
slices. In addition, values of the dimensionless quantity T_c/m_rho are in
closer agreement with those for staggered quarks than was the case at N_t=4. (A
POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM
sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)
|
hep-lat/9207025
| 727,401 |
The impact of the new tau decay data on the various $\tau$ puzzles and on the
possibility of approximate supersymmetry is discussed. The most economical
solution of the problems in $\tau$ decay and that favored by recent new data
supports the existence of gluinos below one GeV.
|
hep-ph/9207254
| 727,401 |
We calculate the triviality bound on the Higgs mass in scalar field theory
models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial}
\approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity.
Limits on observable cutoff effects at four percent in several regularized
models with tunable couplings in the bare action yield triviality bounds
displaying a large degree of universality. Extrapolating from $N=\infty$ to
$N=4$ we conservatively estimate that a Higgs particle with mass up to
$0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff
effects, indicating that strong scalar self interactions in the standard model
are not ruled out.
Note: The full ps file of this preprint is also available via anonymous ftp
to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for
username "anonymous" and for password your name. The file is in the directory
pub/vranas (to go to that directory type: cd pub/vranas) and is called
lrg_n_hig.ps (to get it type: get lrg_n_hig.ps)
|
hep-lat/9207024
| 727,401 |
Motivated by the apparent dependence of string $\sigma$--models on the sum of
spacetime metric and antisymmetric tensor fields, we reconsider gravity
theories constructed from a nonsymmetric metric. We first show that all such
"geometrical" theories homogeneous in second derivatives violate standard
physical requirements: ghost-freedom, absence of algebraic inconsistencies or
continuity of degree-of-freedom content. This no-go result applies in
particular to the old unified theory of Einstein and its recent avatars.
However, we find that the addition of nonderivative, ``cosmological'' terms
formally restores consistency by giving a mass to the antisymmetric tensor
field, thereby transmuting it into a fifth-force-like massive vector but with
novel possible matter couplings. The resulting macroscopic models also exhibit
``van der Waals''-type gravitational effects, and may provide useful
phenomenological foils to general relativity.
|
gr-qc/9207003
| 727,401 |
Three simple examples illustrate properties of path integral amplitudes in
fixed background spacetimes with closed timelike curves: non-relativistic
potential scattering in the Born approximation is non-unitary, but both an
example with hard spheres and the exact solution of a totally discrete model
are unitary.
|
hep-th/9207076
| 727,401 |
We present a multicanonical algorithm for the SU(3) pure gauge theory at the
deconfinement phase transition. We measure the tunneling times for lattices of
size L^3x2 for L=8,10, and 12. In contrast to the canonical algorithm the
tunneling time increases only moderately with L. Finally, we determine the
interfacial free energy applying the multicanonical algorithm.
|
hep-lat/9207026
| 727,402 |
The two lineal gravities --- based on the de Sitter group or a central
extension of the Poincar\'e group in 1+1 dimensions --- are shown to derive
classically from a unique topological gauge theory. This one is obtained after
a dimensional reduction of a Chern--Simons model, which describes pure gravity
in 2+1 dimensions, the gauge symmetry being given by an extension of ISO(2,1).
|
gr-qc/9207004
| 727,402 |
The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models
coupled to gravity is shown to be ${\cal R}={\cal R}_0\otimes {\bf C}
[w,w^{-1}]$ where ${\cal R}_0$ is the ring of ghost number zero operators
generated by two elements and $w$ is an operator of ghost number $-1$. Some
examples are discussed in detail. For these models the currents are also
discussed and their algebra is shown to contain the Virasoro algebra.
|
hep-th/9207078
| 727,402 |
General relativity has previously been extended to incorporate degenerate
metrics using Ashtekar's hamiltonian formulation of the theory. In this letter,
we show that a natural alternative choice for the form of the hamiltonian
constraints leads to a theory which agrees with GR for non-degenerate metrics,
but differs in the degenerate sector from Ashtekar's original degenerate
extension. The Poisson bracket algebra of the alternative constraints closes in
the non-degenerate sector, with structure functions that involve the {\it
inverse} of the spatial triad. Thus, the algebra does {\it not} close in the
degenerate sector. We find that it must be supplemented by an infinite number
ofsecondary constraints, which are shown to be first class (although their
explicit form is not worked out in detail). All of the constraints taken
together are implied by, but do not imply, Ashtekar's original form of
constraints. Thus, the alternative constraints give rise to a different
degenerate extension of GR. In the corresponding quantum theory, the single
loop and intersecting loop holonomy states found in the connection
representation satisfy {\it all} of the constraints. These states are therefore
exact (formal) solutions to this alternative degenerate extension of quantum
gravity, even though they are {\it not} solutions to the usual vector
constraint.
|
gr-qc/9207005
| 727,402 |
It has recently been shown by Goldberg et al that the holonomy group of the
chiral spin-connection is preserved under time evolution in vacuum general
relativity. Here, the underlying reason for the time-independence of the
holonomy group is traced to the self-duality of the curvature 2-form for an
Einstein space. This observation reveals that the holonomy group is
time-independent not only in vacuum, but also in the presence of a cosmological
constant. It also shows that once matter is coupled to gravity, the
"conservation of holonomy" is lost. When the fundamental group of space is
non-trivial, the holonomy group need not be connected. For each homotopy class
of loops, the holonomies comprise a coset of the full holonomy group modulo its
connected component. These cosets are also time-independent. All possible
holonomy groups that can arise are classified, and examples are given of
connections with these holonomy groups. The classification of local and global
solutions with given holonomy groups is discussed.
|
gr-qc/9207006
| 727,402 |
A cosmological model in which the primordial perturbations are provided by
global monopoles and in which the dark matter is cold has several interesting
features. The model is normalized by choosing its single parameter within the
bounds obtained from gravitational wave constraints and by demanding coherent
velocity f1ows of about 600km/sec on scales of $50 h^{-1} Mpc$. Using this
normalization, the model predicts the existence of dominant structures with
mass $2\times 10^{16} M_\odot$ on a scale $35 h^{-1}Mpc$ i.e. larger than the
horizon at $t_{eq}$. The magnitude of the predicted mass function in the
galactic mass range is in good agreement with the observed Schechter function.
|
hep-ph/9207255
| 727,402 |
In this paper we study the proalgebraic completion of mapping class relative
to their maps to the symplectic group. The main result is that the natural map
from the unipotent (a.k.a. Malcev) completion of the Torelli group to the
prounipotent radical of the Sp_g completion of the mapping class group is a non
trivial central extension with kernel isomorphic to Q, at least when g \ge 8.
The theorem is proved by relating the central extension to the line bundle
associated to the archemidean height of the cycle C - C- in the Jacobian of the
curve C. We also develop some of the basic theory of relative completions.
|
alg-geom/9207001
| 727,402 |
We use arguments based on Derrick's theorem to show that the property of
collapse which is the key feature of global texture appears in several field
theory models with broken global O(N) symmetry. Such models do not necessarily
have nontrivial third homotopy group of the vacuum manifold but may give rise
to collapsing global field configurations with properties similar to textures.
It is verified that configurations with planar and cylindrical geometries do
not collapse. The existence of critical parameters for collapse of spherically
symmetric global field configurations is verified both analytically and
numerically.
|
hep-ph/9207256
| 727,402 |
We extend a previous calculation which treated Schwarschild black hole
horizons as quantum mechanical objects to the case of a charged, dilaton black
hole. We show that for a unique value of the dilaton parameter `a', which is
determined by the condition of unitarity of the S matrix, black holes transform
at the extremal limit into strings.
|
hep-th/9207079
| 727,402 |
In this paper, we formulate a generalization of the classical BRST
construction which applies to the case of the reduction of a poisson manifold
by a submanifold. In the case of symplectic reduction, our procedure
generalizes the usual classical BRST construction which only applies to
symplectic reduction of a symplectic manifold by a coisotropic submanifold,
\ie\ the case of reducible ``first class'' constraints. In particular, our
procedure yields a method to deal with ``second-class'' constraints. We
construct the BRST complex and compute its cohomology. BRST cohomology vanishes
for negative dimension and is isomorphic as a poisson algebra to the algebra of
smooth functions on the reduced poisson manifold in zero dimension. We then
show that in the general case of reduction of poisson manifolds, BRST
cohomology cannot be identified with the cohomology of vertical differential
forms.
|
hep-th/9207080
| 727,402 |
We study the critical behaviour of the \SUN{} generalization of the
one-dimensional Hubbard model with arbitrary degeneracy $N$. Using the
integrability of this model by Bethe Ansatz we are able to compute the spectrum
of the low-lying excitations in a large but finite box for arbitrary values of
the electron density and of the Coulomb interaction. This information is used
to determine the asymptotic behaviour of correlation functions at zero
temperature in the presence of external fields lifting the degeneracy. The
critical exponents depend on the system parameters through a $N\times N$
dressed charge matrix implying the relevance of the interaction of charge- and
spin-density waves.
|
cond-mat/9207026
| 727,403 |
We discuss detailed simulations of the non compact abelian model coupled to
light fermions, using a method previously developed that includes the effects
of the fermionic interactions in an effective action. The approximations
involved are related to an expansion in the flavour number. We address the
problem of the (non) triviality of the theory through a study of the analytical
properties of the effective action as a function of the pure gauge energy. New
numerical results for the plaquette energy, chiral condensate and a qualitative
analysis of the phase diagram are also presented.
|
hep-lat/9207027
| 727,403 |
In an effective Lagrangian approach to physics beyond the Standard Model, it
has been argued that imposing $SU(2) \times U(1)$ invariance severely restricts
the discovery potential of future colliders. We exhibit a possible way out in
an extended gauge group context.
|
hep-ph/9207258
| 727,403 |
The non-perturbative ultraviolet divergence of the sine-Gordon model is used
to study the $k^+ = 0$ region of light-cone perturbation theory. The light-cone
vacuum is shown to be unstable at the non-perturbative $\beta^2 = 8\pi$
critical point by a light-cone version of Coleman's variational method. Vacuum
bubbles, which are $k^+=0$ diagrams in light-cone field theory and are
individually finite and non-vanishing for all $\beta$, conspire to generate
ultraviolet divergences of the light-cone energy density. The $k^+ = 0$ region
of momentum also contributes to connected Green's functions; the connected two
point function will not diverge, as it should, at the critical point unless
diagrams which contribute only at $k^+ = 0$ are properly included. This
analysis shows in a simple way how the $k^+ =0$ region cannot be ignored even
for connected diagrams. This phenomenon is expected to occur in higher
dimensional gauge theories starting at two loop order in light-cone
perturbation theory.
|
hep-th/9207082
| 727,403 |
Staggered fermions are constructed for the transverse lattice regularization
scheme. The weak perturbation theory of transverse lattice non-compact QED is
developed in light-cone gauge, and we argue that for fixed lattice spacing this
theory is ultraviolet finite, order by order in perturbation theory. However,
by calculating the anomalous scaling dimension of the link fields, we find that
the interaction Hamiltonian becomes non-renormalizable for $g^2(a) > 4\pi$,
where $g(a)$ is the bare (lattice) QED coupling constant. We conjecture that
this is the critical point of the chiral symmetry breaking phase transition in
QED. Non-perturbative chiral symmetry breaking is then studied in the strong
coupling limit. The discrete remnant of chiral symmetry that remains on the
lattice is spontaneously broken, and the ground state to lowest order in the
strong coupling expansion corresponds to the classical ground state of the
two-dimensional spin one-half Heisenberg antiferromagnet.
|
hep-th/9207083
| 727,403 |
I review the spin dependent structure functions which control dominant
(twist-2) and sub-dominant (twist-3) phenomena in hard processes. Novel effects
associated with chirally odd parton distributions and with transverse
polarization are emphasized.
|
hep-ph/9207259
| 727,403 |
Damour, Deser and McCarthy have claimed that the nonsymmetric gravitational
theory (NGT) is untenable due to curvature coupled ghost modes and bad
asymptotic behavior. This claim is false for it is based on a physically
inaccurate treatment of wave propagation on a curved background and an
incorrect method for extracting asymptotic behavior. We show that the flux of
gravitational radiation in NGT is finite in magnitude and positive in sign.
|
gr-qc/9207007
| 727,403 |
Given a free ideal J of subsets of a set X, we consider games where player
ONE plays an increasing sequence of elements of the sigma completion of J, and
TWO tries to cover the union of this sequence by playing one set at a time from
J. We describe various conditions under which player TWO has has a winning
strategy that uses only information about the most recent k moves of ONE, and
apply some of these results to the Banach-Mazur game.
|
math/9207203
| 727,404 |
The following notes provide an introduction to recent work of Branner,
Hubbard and Yoccoz on the geometry of polynomial Julia sets. They are an
expanded version of lectures given in Stony Brook in Spring 1992. I am indebted
to help from the audience.
Section 1 describes unpublished work by J.-C. Yoccoz on local connectivity of
quadratic Julia sets. It presents only the "easy" part of his work, in the
sense that it considers only non-renormalizable polynomials, and makes no
effort to describe the much more difficult arguments which are needed to deal
with local connectivity in parameter space. It is based on second hand sources,
namely Hubbard together with lectures by Branner and Douady. Hence the
presentation is surely quite different from that of Yoccoz.
Section 2 describes the analogous arguments used by Branner and Hubbard to
study higher degree polynomials for which all but one of the critical orbits
escape to infinity. In this case, the associated Julia set J is never locally
connected. The basic problem is rather to decide when J is totally
disconnected. This Branner-Hubbard work came before Yoccoz, and its technical
details are not as difficult. However, in these notes their work is presented
simply as another application of the same geometric ideas.
Chapter 3 complements the Yoccoz results by describing a family of examples,
due to Douady and Hubbard (unpublished), showing that an infinitely
renormalizable quadratic polynomial may have non-locally-connected Julia set.
An Appendix describes needed tools from complex analysis, including the
Gr\"otzsch inequality.
|
math/9207220
| 727,404 |
The phase shift of the O(4) symmetric $\phi^4$ theory in the symmetric phase
is calculated numerically using the relation between phase shift and energy
levels of two-particle states recently derived by L\"{u}scher. The results
agree with the prediction of perturbation theory. A practical difficulty of the
method for a reliable extraction of the phase shift for large momenta due to
the necessity of a precise determination of excited two-particle energy levels
is pointed out.
|
hep-lat/9207028
| 727,405 |
We give a pedagogical introduction to the differential calculus on quantum
groups by stressing at all stages the connection with the classical case ($q
\rightarrow 1$ limit). The Lie derivative and the contraction operator on forms
and tensor fields are found. A new, explicit form of the Cartan--Maurer
equations is presented. The example of a bicovariant differential calculus on
the quantum group $GL_q(2)$ is given in detail. The softening of a quantum
group is considered, and we introduce $q$-curvatures satisfying q-Bianchi
identities, a basic ingredient for the construction of $q$-gravity and
$q$-gauge theories.
|
hep-th/9207084
| 727,405 |
Deviations from scale invariance resulting from small perturbations of a
general two dimensional conformal field theory are studied. They are expressed
in terms of beta functions for renormalization of general couplings under local
change of scale. The beta functions for homogeneous background are given
perturbatively in terms of the data of the original conformal theory without
any specific assumptions on its nature. The renormalization of couplings to
primary operators and to first descendents is considered as well as that of
couplings of a dilatonic type which involve explicit dependence on world sheet
curvature.
|
hep-th/9207085
| 727,405 |
Early 17th-century mathematical publications of Johann Faulhaber contain some
remarkable theorems, such as the fact that the $r$-fold summation of
$1^m,2^m,...,n^m$ is a polynomial in $n(n+r)$ when $m$ is a positive odd
number. The present paper explores a computation-based approach by which
Faulhaber may well have discovered such results, and solves a 360-year-old
riddle that Faulhaber presented to his readers. It also shows that similar
results hold when we express the sums in terms of central factorial powers
instead of ordinary powers. Faulhaber's coefficients can moreover be
generalized to factorial powers of noninteger exponents, obtaining asymptotic
series for $1^{\alpha}+2^{\alpha}+...+n^{\alpha}$ in powers of
$n^{-1}(n+1)^{-1}$.
|
math/9207222
| 727,406 |
Under the assumption that the color charge can be written in a BRST exact
form, the color confinement mechanism proposed by Kugo and Ojima (KO) explains
the confinement of any colored particles including dynamical quarks and gluons.
This mechanism, however, is known to break down in the Abelian gauge which
treats the maximal Abelian subgroup of the gauge group in a special manner. In
order to study whether the failure of the KO mechanism is particular only to
the Abelian gauge or whether this failure occurs in a wide class of gauges
including the ordinary Lorentz type gauge, we carry out a renormalization group
study of the $SU(2)$ gauge theory in the gauge fixing space. Our gauge fixing
space consists of four distinct regions that are not connected with each other
by renormalization group flows, and we find that the Abelian gauge is {\it
infrared unstable} in three regions which include the Lorentz type gauge. This
suggests that the failure of the KO mechanism is a phenomenon which occurs only
in the Abelian gauge. We also find that the Lorentz gauge is infrared stable.
|
hep-ph/9207260
| 727,406 |
We analize the current data on $\tau$-lepton decays and show that they are
consistent with the Standard Model
|
hep-ph/9207262
| 727,406 |
We consider the possibility that the $\tau$ decay puzzle, if it is confirmed
in future experiments, is a consequence of the Kobayashi-Maskawa mixing in the
leptonic sector
|
hep-ph/9207263
| 727,406 |
We study numerically the gravitational field of a star made of massive and
neutral string states for the case in which the dilaton is massive. The
solution exhibits very simple scaling properties in the dilaton mass. There is
no horizon and the singularity is surrounded by a halo (the physical size of
which is inversely proportional to the dilaton mass) where the scalar curvature
is very large and proportional to the square of the dilaton mass.
|
hep-th/9207087
| 727,406 |
It will be described how to uniquely fix the gauge using Coulomb gauge
fixing, avoiding the problem of Gribov copies. The fundamental modular domain,
which represents a one-to-one representation of the set of gauge invariant
degrees of freedom, is a bounded convex subset of the trans- verse gauge
fields. Boundary identifications are the only remnants of the Gribov copies,
and carry all the information about the topology of the Yang-Mills
configuration space. Conversely, the known topology can be shown to imply that
(on a set of measure zero on the boundary) some points of the boundary coincide
with the Gribov horizon. For the low-lying energies, wavefunctionals can be
shown to spread out "across" certain parts of these boundaries. This is how the
topology of Yang-Mills configuration space has an essential influence on the
low-lying spectrum, in a situation where these non- perturbative effects are
not exponentially suppressed.
This write-up is a short summary, with adequate references, where details on
most of the material I have presented can be found. However, not published
before, is a new observation concerning Henyey's gauge copies.
|
hep-lat/9207029
| 727,406 |
The propagation differential for bosonic strings on a complex torus with
three symmetric punctures is investigated. We study deformation aspects between
two point and three point differentials as well as the behaviour of the
corresponding Krichever-Novikov algebras. The structure constants are
calculated and from this we derive a central extension of the Krichever-Novikov
algebras by means of b-c systems. The defining cocycle for this central
extension deforms to the well known Virasoro cocycle for certain kinds of
degenerations of the torus.
AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40
|
hep-th/9207088
| 727,406 |
The critical behavior of pinned charge density waves (CDW's) is studied as
the threshold for sliding is approached. Using the Fukuyama-Lee-Rice
Hamiltonian with relaxational dynamics, the polarization and linear response
are calculated numerically. ... On the irreversible approach to threshold, the
response due to avalanches triggered by local instabilities dominates the
polarizability, which diverges in one and two dimensions. Characteristic
diverging length scales are studied using finite-size scaling of the
sample-to-sample variations of the threshold field in finite systems and
finite-size effects in the linear polarizability and the irreversible
polarization. A dominant diverging correlation length is found which controls
the threshold field distribution, finite-size effects in the irreversible
polarization, and a cutoff size for the avalanche size distribution. Our
results are compared with those for related models and questions are raised
concerning the relationship of the static critical behavior below threshold to
the dynamic critical behavior in the sliding state above threshold.
|
cond-mat/9207027
| 727,406 |
It is shown that self-dual theories generalize to four dimensions both the
conformal and analytic aspects of two-dimensional conformal field theories. In
the harmonic space language there appear several ways to extend complex
analyticity (natural in two dimensions) to quaternionic analyticity (natural in
four dimensions). To be analytic, conformal transformations should be realized
on $CP^3$, which appears as the coset of the complexified conformal group
modulo its maximal parabolic subgroup. In this language one visualizes the
twistor correspondence of Penrose and Ward and consistently formulates the
analyticity of Fueter.
|
hep-th/9207089
| 727,406 |
Unstable relics with lifetime longer than the age of the Universe could be
the dark matter today. Electrons, photons and neutrinos are a natural outcome
of their decay and could be searched for in cosmic rays and in $\gamma$-ray and
neutrino detectors. I compare the sensitivities of these three types of
searches to the mass and lifetime of a generic unstable particle. I show that
if the relics constitute our galactic halo and their branching ratios into
electron-positrons, photons and neutrinos are comparable, neutrino searches
would probe the longest lifetimes for masses $\simge 40 \TeV$, while
electron-positron searches would be better but more uncertain for lighter
particles. If instead the relics are not clustered in our halo, neutrinos are
more sensitive a probe than $\gamma$-rays for masses $\simge 700 \GeV$. A $ 1
\sqkm $ neutrino telescope should be able to explore lifetimes up to $ \sim
10^{30} \sec $ while searching for neutrinos from unstable particles above the
atmospheric background.
|
hep-ph/9207261
| 727,406 |
We consider the general procedure for proving no-hair theorems for static,
spherically symmetric black holes. We apply this method to the abelian Higgs
model and find a proof of the no-hair conjecture that circumvents the
objections raised against the original proof due to Adler and Pearson.
|
gr-qc/9207008
| 727,406 |
I show that factorization for hard processes in QCD is also valid when the
detected particles are polarized, and that the proof of the theorem determines
the operator form for the parton densities. Particular attention is given to
the case of transversely polarized incoming hadrons.
|
hep-ph/9207265
| 727,406 |
We examine gravitational waves in an isolated axi--symmetric reflexion
symmetric NGT system. The structure of the vacuum field equations is analyzed
and the exact solutions for the field variables in the metric tensor are found
in the form of expansions in powers of a radial coordinate. We find that in the
NGT axially symmetric case the mass of the system remains constant only if the
system is static (as it necessarily is in the case of spherical symmetry). If
the system radiates, then the mass decreases monotonically and the energy flux
associated with waves is positive.
|
gr-qc/9207009
| 727,406 |
We investigate the use of global demons, a `canonical dynamics', as an
approach to simulating lattice regularized field theories. This
deterministically chaotic dynamics is non-local and non-Hamiltonian, and
preserves the canonical measure rather than $\delta(H-E)$. We apply this
inexact dynamics to the 2D XY model, comparing to various implementations of
hybrid Monte Carlo, focusing on critical exponents and critical slowing down.
In addition, we discuss a scheme for making energy non-conserving dynamical
algorithms exact without the use of a Metropolis hit.
|
hep-lat/9207030
| 727,406 |
We show that multivariable colored link invariants are derived from the roots
of unity representations of $U_q(g)$. We propose a property of the
Clebsch-Gordan coefficients of $U_q(g)$, which is important for defining the
invariants of colored links. For $U_q(sl_2) we explicitly prove the property,
and then construct invariants of colored links and colored ribbon graphs, which
generalize the multivariable Alexander polynomial.
|
hep-th/9207090
| 727,407 |
A method is developed whereby spinor helicity techniques can be used to
simplify the calculation of loop amplitudes. This is achieved by using the
Feynman-parameter representation where the offending off-shell loop momenta do
not appear. Background Feynman gauge also helps to simplify the calculations.
This method is applicable to any Feynman diagram with any number of loops as
long as the external masses can be ignored, and it is at least as efficient as
the string technique in the special circumstances when the latter can be used.
In order to minimize the very considerable algebra encountered in non-abelian
gauge theories, graphical methods are developed for most of the calculations.
This enables the large number of terms encountered to be organized visually in
the Feynman diagram without the necessity of having to write down any of them
algebraically. A one-loop four-gluon amplitude in a particular helicity
configuration is computed explicity to illustrate the method.
|
hep-ph/9207266
| 727,407 |
We show that the isometries of the manifold of scalars in $N=2$ supergravity
in $d=5$ space-time dimensions can be broken by the supergravity interactions.
The opposite conclusion holds for the dimensionally reduced $d=4$ theories,
where the isometries of the scalar manifold are always symmetries of the full
theory. These spaces, which form a subclass of the {\em special} K\"ahler
manifolds, are relevant for superstring compactifications.
|
hep-th/9207091
| 727,407 |
Using the tetrad formalism, we carry out the separation of variables for the
massive complex Dirac equation in the gravitational and electromagnetic field
of a four-parameter (mass, angular momentum, electric and magnetic charges)
black hole.
|
gr-qc/9207010
| 727,407 |
We discuss the implications of global symmetries on the radiative corrections
to the Higgs sector. We focus on two examples: the charged Higgs mass in the
minimal supersymmetric model and the Higgs couplings to vector boson pairs. In
the first case, we find that in the absence of squark mixing a global
SU(2)$\times$SU(2) symmetry protects the charged Higgs mass from corrections of
${\cal O}(g^2m^4_t/m^2_W)$. In the second case, it is the {\it custodial}
symmetry which plays an analogous role in constraining the fermion-mass
dependence of the radiative corrections.
|
hep-ph/9207267
| 727,408 |
We discuss the problem of N anyons in harmonic well, and derive the
semi-classical spectrum as an exactly solvable limit of the many-anyon
Hamiltonian. The relevance of our result to the solution of the anyon-gas model
is discussed.
|
hep-th/9207098
| 727,408 |
For the many-anyon system in external magnetic field, we derive the energy
spectrum as an exact solution of the quantum eigenvalue problem with particular
topological constraints. Our results agree with the numerical spectra recently
obtained for the 3- and the 4-anyon systems.
|
hep-th/9207099
| 727,408 |
In the framework of the Caldeira-Leggett model of dissipative quantum
mechanics, we investigate the effects of the interaction of the thermal
reservoir with an external field. In particular, we discuss how the interaction
modifies the conservative dynamics of the central particle, and the mechanism
of dissipation. We briefly comment on possible observable consequencies.
|
hep-th/9207100
| 727,408 |
We quantize $sl_n$ Toda field theories in a periodic lattice. We find the
quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the
case of the defining representation. In the $sl_3$ case we extend the analysis
also to the second fundamental representation. We clarify, in particular, the
relation of Jimbo and Rosso's quantum $R$ matrix with the quantum $R$ matrix in
the Bloch wave basis.
|
hep-th/9207101
| 727,408 |
For a system near a second order phase transition, the probability
distribution for the order parameter can be given a finite size scaling form.
This fact is used to compare the finite temperature phase transition for the
Wilson lines in d=3+1 SU(2) lattice gauge theory with the phase transition in
d=3 phi^4 field theory. I exhibit the finite size scaled probability
distributions in the form of a function of two variables (the reduced
`temperature' and the magnetization) for both models. The two surfaces look
identical, and an analysis of the errors also suggests that they are the same.
This strengthens the idea that the SU(2) effective line theory is in the Ising
universality class. I argue for the wider application of the method used here.
|
hep-lat/9207031
| 727,408 |
The neutral kaon system is a sensitive probe of quantum mechanics. We revive
a parametrization of non-quantum-mechanical effects that is motivated by
considerations of the nature of space-time foam, and show how it can be
constrained by new measurements of $K_L \rightarrow 2\pi$ and $K_{L,S}$
semileptonic decays at LEAR or a $\phi$ factory.
|
hep-ph/9207268
| 727,408 |
I report on recent developments in the heavy-quark effective theory and its
application to $B$ meson decays. The parameters of the effective theory, the
spin-flavor symmetry limit, and the leading symmetry-breaking corrections to it
are discussed. The results of a QCD sum rule analysis of the universal
Isgur-Wise functions that appear at leading and subleading order in the $1/m_Q$
expansion are presented. I illustrate the phenomenological applications of this
formalism by focusing on two specific examples: the determination of $V_{cb}$
from the endpoint spectrum in semileptonic decays, and the study of
spin-symmetry violating effects in ratios of form factors. I also briefly
comment on nonleptonic decays.
|
hep-ph/9207270
| 727,408 |
Higgs production from $Z$ decay in supersymmetry with spontaneous broken R
parity proceeds mostly by the Bjorken process as in the standard model.
However, the corresponding production rates can be weaker than in the standard
model (SM), especially in the low mass region. This will substantially weaken
the Higgs boson mass limits derived from LEP1. More strikingly, the main Higgs
decay channel is "invisible", over most of the mass range accessible to LEP1,
leading to events with large missing energy carried by majorons. This
possibility should be taken into account in the planning of Higgs boson search
strategies not only at LEP but also at high energy supercolliders.
|
hep-ph/9207269
| 727,408 |
Shelah introduced the revised countable support (RCS) iteration to iterate
semiproperness. This was an endpoint in the search for an iteration of a weak
condition, still implying that aleph1 is preserved.
Dieter Donder found a better manageable approach to this iteration, which is
presented here.
|
math/9207204
| 727,409 |
Degenerations of Lie algebras of meromorphic vector fields on elliptic curves
(i.e. complex tori) which are holomorphic outside a certain set of points
(markings) are studied. By an algebraic geometric degeneration process certain
subalgebras of Lie algebras of meromorphic vector fields on P^1 the Riemann
sphere are obtained. In case of some natural choices of the markings these
subalgebras are explicitly determined. It is shown that the number of markings
can change. AMS subject classification (1991): 17B66, 17B90, 14F10, 14H52,
30F30, 81T40
|
hep-th/9207104
| 727,409 |
The standard electroweak final-state interaction induces a false T-odd
correlation in the top-quark semileptonic decay. The correlation parameter is
calculated in the standard model and found to be considerably larger than those
that could be produced by genuine T-violation effects in a large class of
theoretical models.
|
hep-ph/9207271
| 727,409 |
We show how the double cohomology of the String and Felder BRST charges
naturally leads to the ring structure of $c<1$ strings. The chiral ring is a
ring of polynomials in two variables modulo an equivalence relation of the form
$x^p \simeq y^{p+1}$ for the (p+1,p) model. We also study the states
corresponding to the edges of the conformal grid whose inclusion is crucial for
the closure of the ring. We introduce candidate operators that correspond to
the observables of the matrix models. Their existence is motivated by the
relation of one of the screening operators of the minimal model to the zero
momentum dilaton.
|
hep-th/9207109
| 727,409 |
If an evaporating black hole does not settle down to a non radiating remnant,
a description by a semi classical Lorentz metric must contain either a naked
singularity or what we call a thunderbolt, a singularity that spreads out to
infinity on a spacelike or null path. We investigate this question in the
context of various two dimensional models that have been proposed. We find that
if the semi classical equations have an extra symmetry that make them solvable
in closed form, they seem to predict naked singularities but numerical
calculations indicate that more general semi classical equations, such as the
original CGHS ones give rise to thunderbolts. We therefore expect that the semi
classical approximation in four dimensions will lead to thunderbolts. We
interpret the prediction of thunderbolts as indicating that the semi classical
approximation breaks down at the end point of black hole evaporation, and we
would expect that a full quantum treatment would replace the thunderbolt with a
burst of high energy particles. The energy in such a burst would be too small
to account for the observed gamma ray bursts.
|
hep-th/9207105
| 727,409 |
We study the electromagnetic pion form factor and the VV - AA two point
function for momenta -(600 MeV)^2 < q^2 < (600 MeV)^2 and we note the
similarity between vector meson dominance and two versions of the free
constituent quark model. The similarity is more striking when the momentum
dependence of the quark mass is taken into account. We consider the
implications for QCD and other theories.
|
hep-ph/9207272
| 727,409 |
Quantum Electrodynamics can be formulated as the theory of an antisymmetric
tensor gauge field. In this formulation the topological current of this field
appears as an additional source for the electromagnetic field. The topological
charge therefore acts physically as an electric charge. The topologically
nontrivial, electrically charged sector contains massless quantum states
orthogonal to the vacuum in spite of the absence of classical topological
solutions. These states are created by a gauge invariant local operator and can
be interpreted as coherent states of photons. The obtainment of a quantity like
charge, which is usually associated with matter, as a property of some peculiar
states of the gauge field points towards the possibility of describing both the
matter and the fields which mediate its interactions within the same unified
framework.
|
hep-th/9207106
| 727,409 |
Chiral densities obeying a $w_{\infty}$ Poisson--bracket algebra are
constructed for the $2+1\,\, A_{\infty}$ -- Toda field theory, using its
alternative $w_{\infty}$ -- Toda representation. They are obtained from formal
traces of powers of the Lax operator. The spin 2 and 3 currents are explicitely
derived, and the consistency of their Poisson algebra is checked.
|
hep-th/9207107
| 727,409 |
The lowest moment of the twist-two, chiral-odd parton distribution $h_1(x)$
of the nucleon can be related to the so-called ``tensor charges'' of the
nucleon. We consider the tensor charges in the Skyrme model, and find that in
the large-$N_c$, SU(3)-symmetric limit, the model predicts that the octet
isosinglet tensor charge, $g^8_T$, is of order $1/N_c$ with respect to the
octet isovector tensor charge, $g^3_T$. The predicted $F/D$ ratio is then 1/3,
in the large-$N_c$ limit. These predictions coincide with the Skyrme model
predictions for the octet ${\it axial}$ charges, $g^8_A$ and $g^3_A$. (The
prediction $F/D=1/3$ for the axial charges differs from the commonly quoted
prediction of 5/9, which is based on an inconsistent treatment of the
large-$N_c$ limit.) The model also predicts that the singlet tensor charge,
$g^0_T$, is of order $1/N_c$ with respect to $g^3_T$.
|
hep-ph/9207274
| 727,409 |
We show how to obtain the two-dimensional black hole action by dimensional
reduction of the three-dimensional Einstein action with a non-zero cosmological
constant. Starting from the Chern-Simons formulation of 2+1 gravity, we obtain
the 1+1 dimensional gauge formulation given by Verlinde. Remarkably, the
proposed reduction shares the relevant features of the formulation of Cangemi
and Jackiw, without the need for a central charge in the algebra. We show how
the Lagrange multipliersin these formulations appear naturally as the remnants
of the three dimensional connection associated to symmetries that have been
lostin the dimensional reduction. The proposed dimensional reduction involves a
shift in the three dimensional connection whose effect is to make the length of
the extra dimension infinite.
|
hep-th/9207108
| 727,409 |
We show that the equivalence theorem approximating one-loop gauge sector
diagrams by including only Goldstone bosons in the loop gives a remarkably poor
approximation to the amplitude for the decay $H\rightarrow \gamma \gamma $ and
for the process $\gamma \gamma \rightarrow HH$. At one loop, large logarithms
can arise that evade power counting arguments.
|
hep-ph/9207275
| 727,409 |
Let m be the least cardinal k such that MA(k) fails. The only known model for
"m is singular" was constructed by Kunen. In Kunen's model cof(m)=omega_1. It
is unknown whether "omega_1 < cof(m) < m" is consistent. The purpose of this
paper is to present a proof of Kunen's result and to identify the difficulties
of generalizing this result to an arbitrary uncountable cofinality.
|
math/9207205
| 727,410 |
In the lattice CP(N) models we studied the problems related to the measure of
the topological susceptibility and the string tension . We perfomed numerical
simulations at N=4 and N=10. In order to test the universality, we adopted two
different lattice formulations. Scaling and universality tests led to the
conclusion that at N=10 the geometrical approach gives a good definition of
lattice topological susceptibility. On the other hand, N=4 proved not to be
large enough to suppress the unphysical configurations, called dislocations,
contributing to the topological susceptibility. We obtained other
determinations of the topological susceptibility by the field theoretical
method, wich relies on a local definition of the lattice topological charge
density, and the cooling method. They gave quite consistent results, showing
scaling and universality. The large-N expansion predicts an exponential area
law behavior for sufficiently large Wilson loops, which implies confinement,
due to the dynamical matter fields and absence of the screening phenomenon. We
determined the string tension, without finding evidence of screening effects.
|
hep-lat/9207032
| 727,410 |
Causal rigid particles whose action includes an {\it arbitrary} dependence on
the world-line extrinsic curvature are considered. General classes of solutions
are constructed, including {\it causal tachyonic} ones. The Hamiltonian
formulation is developed in detail except for one degenerate situation for
which only partial results are given and requiring a separate analysis.
However, for otherwise generic rigid particles, the precise specification of
Hamiltonian gauge symmetries is obtained with in particular the identification
of the Teichm$\ddot{\rm u}$ller and modular spaces for these systems. Finally,
canonical quantisation of the generic case is performed paying special
attention to the phase space restriction due to causal propagation. A mixed
Lorentz-gravitational anomaly is found in the commutator of Lorentz boosts with
world-line reparametrisations. The subspace of gauge invariant physical states
is therefore not invariant under Lorentz transformations. Consequences for
rigid strings and membranes are also discussed.
|
hep-th/9207110
| 727,410 |
There has been some confusion concerning the number of $(1,1)$-forms in
orbifold compactifications of the heterotic string in numerous publications. In
this note we point out the relevance of the underlying torus lattice on this
number. We answer the question when different lattices mimic the same physics
and when this is not the case. As a byproduct we classify all symmetric
$Z_N$-orbifolds with $(2,2)$ world sheet supersymmetry obtaining also some new
ones.
|
hep-th/9207111
| 727,410 |
We suggest a method to compute leading contribution at Planckian energies for
superstring scattering amplitudes of any genus. In particular we test the
method at one-loop level by comparison with previous result for the Regge
trajectory renormalization. Modular invariance of these asymptotic terms are
also discussed.
|
hep-th/9207112
| 727,410 |
The (1+1)-dimensional bosonization relations for fermionic mass terms are
derived by choosing a specific gauge in an enlarged gauge-invariant theory
containing both fermionic and bosonic fields. The fermionic part of the
generating functional subject to the gauge constraint can be cast into the form
of a strongly coupled Schwinger model, which can be solved exactly. The
resulting bosonic theory coupled to the scalar sources then exhibits directly
the bosonic counterparts of the fermionic scalar and pseudoscalar mass
densities.
|
hep-th/9207114
| 727,410 |
Corrections to the semiclassical approximation in nearly forward Planckian
energy collisions are here reconsidered. Starting from the one-loop superstring
amplitude, we are able to disentangle the first subleading high-energy
contribution at large impact parameters, and we thus directly compute the
one-loop correction to the superstring eikonal. We finally argue, on the basis
of analyticity and unitarity, that gravitinos do not contribute at all to the
large distance two-loop ACV correction, which thus acquires a universal
``classical'' interpretation.
|
hep-th/9207113
| 727,410 |
In order to investigate the Higgs mechanism nonperturbatively, we compute the
Gaussian effective potential (GEP) of the U(1) Higgs model ("scalar
electrodynamics"). We show that the same simple result is obtained in three
different formalisms. A general covariant gauge is used, with Landau gauge
proving to be optimal. The renormalization generalizes the "autonomous"
renormalization for lambda-phi^4 theory and requires a particular relationship
between the bare gauge coupling e_B and the bare scalar self- coupling
lambda_B. When both couplings are small, then lambda is proportional to e^4 and
the scalar/vector mass-squared ratio is of order e^2, as in the classic 1-loop
analysis of Coleman and Weinberg. However, as lambda increases, e reaches a
maximum value and then decreases, and in this "nonperturbative" regime the
Higgs scalar can be much heavier than the vector boson. We compare our results
to the autonomously renormalized 1-loop effective potential, finding many
similarities. The main phenomenological implication is a Higgs mass of about 2
TeV.
|
hep-ph/9207276
| 727,410 |
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