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The cutoff dependence of the Scalar Sector of the Minimal Standard Model can
result in an increase of the existing triviality bound estimates of the Higgs
mass. We present a large $N$ calculation and some preliminary N=4 results that
suggest that the increase can be as large as 30%, resulting to a bound of about
850 G eV.
|
hep-lat/9201004
| 727,296 |
We present preliminary results from the 1991 HEMCGC simulations with
staggered dynamical fermions on a $16^3 \times 32$ lattice at $\beta = 5.6$
with sea quark masses $am_q = 0.025$ and 0.01. The spectroscopy was done both
for staggered valence quarks with mass equal to the sea quark masses and for
Wilson valence quarks at six different values for $\kappa$, 0.1320, 0.1410,
0.1525, 0.1565, 0.1585, and 0.1600. In addition to the measurements performed
in our earlier work, we also measured the $\Delta$ and other `extended' hadrons
for staggered valence quarks and pseudo-scalar decay constants and vector meson
matrix elements, the wave function at the origin, for Wilson valence quarks.
|
hep-lat/9201005
| 727,296 |
We explore a new approach to the path integral for a latticized quantum
theory. This talk is based on work with N. Khuri and H. Ren.
|
hep-lat/9201006
| 727,296 |
We describe recent results obtained as part of the High Energy Monte Carlo
Grand Challenge (HEMCGC) project concerning the behaviour of lattice QCD with
light dynamical Wilson quarks. We show that it is possible to reach regions of
parameter space with light pions $m_\pi\ll0.2/a$, but that the equilibration
time for such a system is at least of the order of 1,000 unit-length Hybrid
Monte Carlo (HMC) trajectories (about a Gigaflop/sec-year). If the Hybrid
Molecular Dynamics (HMD) algorithm is used with the same parameters it gives
incorrect results.
|
hep-lat/9201007
| 727,296 |
Using the recently proposed multicanonical ensemble, we perform Monte Carlo
simulation for the 2d 7-state Potts model and calculate its surface free energy
density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order
of magnitude smaller than other estimates in the recent literature. Relying on
existing Monte Carlo data, we also give a preliminary estimate for the surface
tension of 4d SU(3) lattice gauge theory with $L_t=2$.
|
hep-lat/9202001
| 727,296 |
The distance scale for a quantum field theory is the correlation length
$\xi$, which diverges with exponent $\nu$ as the bare mass approaches a
critical value. If $t=m^{2}-m_{c}^{2}$, then $\xi=m_{P}^{-1} \sim t^{-\nu}$ as
$t \to 0$. The two-point function of a scalar field has a random walk
representation. The walk takes place in a background of fluctuations (closed
walks) of the field itself. We describe the connection between properties of
the walk and of the two-point function. Using the known behavior of the two
point function, we deduce that the dimension of the walk is $d_{w}=\phi / \nu$
and that there is a singular relation between $t$ and the energy per unit
length of the walk $\theta \sim t^{\phi}$ that is due to the singular behavior
of the background at $t=0$. ($\phi$ is a computable crossover exponent.)
|
hep-lat/9202002
| 727,296 |
Lattice QCD with 2 light staggered quark flavours is being simulated on a
$16^3\times8$ lattice to study the transition from hadronic matter to a quark
gluon plasma. We have completed runs at $m_q=0.0125$ and are extending this to
$m_q=0.00625$. We also examine the addition of a non-dynamical "strange" quark.
Thermodynamic order parameters are being measured across the transition and
further into the plasma phase, as are various screening lengths. No evidence
for a first order transition is seen, and we estimate the transition
temperature to be $TY_c=143(7) MeV$.
|
hep-lat/9202003
| 727,296 |
Relying on the recently proposed multicanonical algorithm, we present a
numerical simulation of the first order phase transition in the 2d 10-state
Potts model on lattices up to sizes $100\times100$. It is demonstrated that the
new algorithm $lacks$ an exponentially fast increase of the tunneling time
between metastable states as a function of the linear size $L$ of the system.
Instead, the tunneling time diverges approximately proportional to $L^{2.65}$.
Thus the computational effort as counted per degree of freedom for generating
an independent configuration in the unstable region of the model rises
proportional to $V^{2.3}$, where $V$ is the volume of the system. On our
largest lattice we gain more than two orders of magnitude as compared to a
standard heat bath algorithm. As a first physical application we report a high
precision computation of the interfacial tension.
|
hep-lat/9202004
| 727,296 |
A Monte Carlo simulation of the O(4) $\lambda \phi^4$ theory in the broken
phase is performed on a hypercubic lattice in search of an I=1, J=1 resonance.
The region of the cutoff theory where the interaction is strong is investigated
since it is there that a resonance would be expected to have a better chance to
form. In that region the presence of an I=1, J=1 resonance with mass below the
cutoff is excluded.
|
hep-lat/9203001
| 727,296 |
We modified the recently proposed multicanonical MC algorithm for the case of
a magnetic field driven order--order phase transition. We test this {\it
multimagnetic} Monte Carlo algorithm for the D=2 Ising model at $\beta=0.5$ and
simulate square lattices up to size $100 \times 100$. On these lattices with
periodic boundary conditions it is possible to enhance the appearance of
order-order interfaces during the simulation by many orders of magnitude as
compared to the standard Monte Carlo simulation.
|
hep-lat/9203002
| 727,296 |
We present a recursive procedure to calculate the parameters of the recently
introduced multicanonical ensemble and explore the approach for spin glasses.
Temperature dependence of the energy, the entropy and other physical quantities
are easily calculable and we report results for the zero temperature limit. Our
data provide evidence that the large $L$ increase of the ergodicity time is
greatly improved. The multicanonical ensemble seems to open new horizons for
simulations of spin glasses and other systems which have to cope with
conflicting constraints.
|
hep-lat/9204001
| 727,296 |
The low energy limit of an axion field coupled to gauge fields is
investigated through the behaviour of the gauge field propagator in a local
vaccum angle background. The local (singular) part of the effective action for
the axion field is calculated at one loop level. In the case of a timelike,
linearly growing axion field, representing a massive axion, we give an
asymptotic expansion of the causal propagator and we solve nonlocally for the
first coefficient. We show that, for a generic axionic background, short
distance propagation of the gauge fields is well defined.
|
hep-th/9204021
| 727,297 |
Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar
formulation, when the spatial manifold is a torus. We have found a set of
globally defined observables, forming a closed algebra. This allowed us to
solve the quantum constraints, and to show that the reduced phase space of the
Ashtekar formulation is greater then the corresponding space of the Witten
formulation. Furthermore, we have found a globally defined time variable which
satisfies all the requiriments of an extrinsic time variable in quantum
gravity.
|
hep-th/9204022
| 727,297 |
We give an argument that magnetic monopoles should not exist. It is based on
the concept of the index of a vector field. The thrust of the argument is that
indices of vector fields are invariants of space-time orientation and of
coordinate changes, and thus physical vector fields should preserve indices.
The index is defined inductively by means of an equation called the Law of
Vector Fields. We give extended philosophical arguments that this Law of Vector
Fields should play an important role in mathematics, and we back up this
contention by using it in a mechanical way to greatly generalize the
Gauss--Bonnet theorem and the Brouwer fixed point theorem and get new proofs of
many other theorems. We also give some other suggestions for using the Law and
index in physics.
|
hep-th/9204087
| 727,297 |
A resummed perturbative expansion is used to obtain the self-energy in the
high-temperature \(g^2\phi^4\) field theory model up to order $g^4$. From this
the zero momentum pole of the effective propagator is evaluated to determine
the induced thermal mass and damping rate for the bosons in the plasma to order
$g^3$. The calculations are performed in the imaginary time formalism and a
simple diagrammatic analysis is used to identify the relevant diagrams at each
order. Results are compared with similar real-time calculations found in the
literature.
|
hep-ph/9204216
| 727,298 |
We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3$
algebra (its classical version) in terms of the spin 1 and spin 2
supercurrents. Two closely related types of the Feigin-Fuchs representation for
these supercurrents are found: via two chiral spin $\frac{1}{2}$ superfields
generating $N=2$ extended $U(1)$ Kac-Moody algebras and via two free chiral
spin 0 superfields. We also construct a one-parameter family of $N=2$ super
Boussinesq equations for which $N=2$ super-$W_3$ provides the second
hamiltonian structure.
|
hep-th/9204023
| 727,298 |
Proposals that $O(d,d)$ boosts of trivial backgrounds lead to non-trivial
conformally invariant backgrounds are checked to two loop order. We find that
conformal invariance can be achieved by adding simple higher order corrections
to the metric and dilaton.
|
hep-th/9204024
| 727,298 |
We describe the duality group $\Gamma=SU(3,3,Z)$ for the Narain lattice of
the $T^6/Z_3$ orbifold and its action on the corresponding moduli space. A
symplectic embedding of the momenta and winding numbers allows us to connect
the orbifold lattice to the special geometry of the moduli space. As an
application, a formal expression for an automorphic function, which is a
candidate for a non--perturbative superpotential, is given.
|
hep-th/9204040
| 727,298 |
We consider the realization of N=2 superconformal models in terms of free
first-order $(b,c,\beta,\gamma)$-systems, and show that an arbitrary
Landau-Ginzburg interaction with quasi-homogeneous potential can be introduced
without spoiling the (2,2)-superconformal invariance. We discuss the
topological twisting and the renormalization group properties of these
theories, and compare them to the conventional topological Landau-Ginzburg
models. We show that in our formulation the parameters multiplying deformation
terms in the potential are flat coordinates. After properly bosonizing the
first-order systems, we are able to make explicit calculations of topological
correlation functions as power series in these flat coordinates by using
standard Coulomb gas techniques. We retrieve known results for the minimal
models and for the torus.
|
hep-th/9204041
| 727,298 |
We study a general class of two-dimensional theories of the dilaton-gravity
type inspired by string theory and show that they admit charged
multiple-horizon black holes. These solutions are proved to satisfy scalar
no-hair theorems.
|
hep-th/9204026
| 727,298 |
We show that the Halperin-Haldane SQHE wave function can be written in the
form of a product of a wave function for charged semions in a magnetic field
and a wave function for the Chiral Spin Liquid of neutral spin-$\12$ semions.
We introduce field-theoretic model in which the electron operators are
factorized in terms of charged spinless semions (holons) and neutral spin-$\12$
semions (spinons). Broken time reversal symmetry and short ranged spin
correlations lead to $SU(2)_{k=1}$ Chern-Simons term in Landau-Ginzburg action
for SQHE phase. We construct appropriate coherent states for SQHE phase and
show the existence of $SU(2)$ valued gauge potential. This potential appears as
a result of ``spin rigidity" of the ground state against any displacements of
nodes of wave function from positions of the particles and reflects the
nontrivial monodromy in the presence of these displacements. We argue that
topological structure of $SU(2)_{k=1}$ Chern-Simons theory unambiguously
dictates {\it semion} statistics of spinons.
|
cond-mat/9204002
| 727,298 |
A new class of singlet superconductors with a gap function $\Delta(\bk,
\omega_n)$ which is {\it odd} in both momentum and Matsubara frequency is
considered. Some of the physical properties of this superconductivity are
discussed and it is argued that: i) the electron-phonon interaction can produce
this kind of pairing, ii) in many cases there is no gap in the quasiparticle
spectrum, iii) these superconductors will exhibit a Meissner effect.
|
cond-mat/9204003
| 727,298 |
It is shown that the Dirac operator in the background of a magnetic
%Reissner-Nordstr\"om black hole and a Euclidean vortex possesses normalizable
zero modes in theories containing superconducting cosmic strings. One
consequence of these zero modes is the presence of a fermion condensate around
magnetically charged black holes which violates global quantum numbers.
|
hep-th/9204025
| 727,298 |
Picture changed operators are discussed in $N=2$ strings with space-time
signature $(2,2)$. A gauge symmetry algebra is derived in a background of torus
space-time $T^{2,2}$ and its simple representation on the picture changed
operators is given. Simple Ward identities associated with the gauge algebra
and their consequences for three and four point amplitudes of arbitrary loops
are also discussed.
|
hep-th/9204027
| 727,299 |
A three dimensional generally covariant theory is described that has a 2+1
canonical decomposition in which the Hamiltonian constraint, which generates
the dynamics, is absent. Physical observables for the theory are described and
the classical and quantum theories are compared with ordinary 2+1 gravity.
|
hep-th/9204029
| 727,299 |
The normal form theorem, proved in R. Laver, On the left distributive law and
the freeness of an algebra of elementary embeddings, Advances in Mathematics 91
(1992), 209-231, for the free algebra $\Cal A$ on one generator $x$ satisfying
the left distributive law $a(bc) = (ab)(ac)$ is extended by showing that
members of $\Cal A$ can be put into a "division form."
|
math/9204203
| 727,301 |
Let $j:V_\lambda---> V_\lambda$ be an elementary embedding, with critical
point $\kappa$, and let $f(n)$ be the number of critical points of embeddings
in the algebra generated by $j$ which lie between $j^n(\kappa)$ and
$j^{n+1}(\kappa)$. It is shown that $f(n)$ is finite for all $n$.
|
math/9204204
| 727,301 |
Various questions posed by P. Nyikos concerning ultrafilters on $\omega$ and
chains in the partial order $(\omega,<^*)$ are answered. The main tool is the
oracle chain condition and variations of it.
|
math/9204205
| 727,301 |
We have calculated the decay rates of the $B_s$ meson in a number of
exclusive two--body decay channels using the Bauer--Stech--Wirbel model for
current matrix elements. The influence of the free parameters of the model on
the predictions is studied. The total branching ratio of the $B_s$ into final
states which only contain stable charged particles is found to be about
$10^{-3}$.
|
hep-ph/9204217
| 727,301 |
We calculate the S parameter of the standard model at one loop of fermions,
using three different regularizations (dimensional, Pauli-Villars and lattice)
and find an extra contribution to the S parameter besides the standard one for
each case. This shows that the extra contribution recently reported for the
lattice regularization is {\it not} necessarily tied to the non-decoupling
effect of fermion doublers. We argue that the extra contribution should be
subtracted in the renormalizable perturbative expansion.
|
hep-ph/9204218
| 727,301 |
We perform Monte Carlo simulations using the Wolff cluster algorithm of the
q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of
spherical topology with up to 5000 nodes. We find that the measured critical
exponents are in reasonable agreement with those from the exact solution of the
Ising model and with those calculated from KPZ scaling for q=3,4 where no exact
solution is available. Using Binder's cumulant we find that the q=10 Potts
model displays a first order phase transition on a dynamical graph, as it does
on a fixed lattice. We also examine the internal geometry of the graphs
generated in the simulation, finding a linear relationship between ring length
probabilities and the central charge of the Potts model
|
hep-lat/9204002
| 727,301 |
A recent study of supersymmetric domain walls in $N=1$ supergravity theories
revealed a new class of domain walls interpolating between supersymmetric vacua
with different non-positive cosmological constants. We classify three classes
of domain wall configurations and study the geodesic structure of the induced
space-time. Motion of massive test particles in such space-times shows that
these walls are always repulsive from the anti-deSitter (AdS) side, while on
the Minkowski side test particles feel no force. Freely falling particles far
away from a wall in an AdS vacuum experience a constant proper acceleration,
\ie\ they are Rindler particles. A new coordinate system for discussing AdS
space-time is presented which eliminates the use of a periodic time-like
coordinate.
|
hep-th/9204031
| 727,301 |
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it
multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of
spherical topology in order to investigate the $c>1$ region of two-dimensional
quantum gravity. Contrary to naive expectation we find no obvious signs of
pathological behaviour for $c>1$. We discuss the results in the light of
suggestions that have been made for a modified DDK ansatz for $c>1$.
|
hep-lat/9204003
| 727,301 |
We find the rules which count the energy levels of the 3 state
superintegrable chiral Potts model and demonstrate that these rules are
complete. We then derive the complete spectrum of excitations in the
thermodynamic limit in the massive phase and demonstrate the existence of
excitations which do not have a quasi-particle form. The physics of these
excitations is compared with the BCS superconductivity spectrum and the
counting rules are compared with the closely related $S=1$ XXZ spin chain.
|
cond-mat/9204004
| 727,301 |
It is proposed that gamma-ray bursts are created in the mergers of double
neutron star binaries and black hole neutron star binaries at cosmological
distances. Bursts with complex profiles and relatively long durations are the
result of magnetic flares generated by the Parker instability in a post-merger
differentially-rotating disk. Some bursts may also be produced through
neutrino-antineutrino annihilation into electrons and positrons. In both cases,
an optically thick fireball of size $\sles\ 100$ km is initially created, which
expands ultrarelativistically to large radii before radiating. Several previous
objections to the cosmological merger model are eliminated. It is predicted
that $\gamma$-ray bursts will be accompanied by a burst of gravitational
radiation from the spiraling-in binary which could be detected by LIGO.
|
astro-ph/9204001
| 727,301 |
The interaction of quarkonium with nuclei is studied in the $m_Q\rightarrow
\infty$ limit of QCD, where the binding energy is found to be exactly
computable. The dominant contribution to the interaction is from two-gluon
operators. The forward matrix elements of these two-gluon operators can be
determined from the QCD scale anomaly, and from deep inelastic scattering. We
apply our results to the $\Upsilon$ and $J/\psi$, treating the $\qqbar$
interaction as purely Coulombic. We find the $\Upsilon$ binds in nuclear matter
with a binding energy of a few $\mev$, while for the $J/\psi$ binding is of
order 10 $\mev$. For the $J/\psi$ in particular we expect confinement effects
to produce large corrections to this result.
|
hep-ph/9204219
| 727,301 |
We study the stability under perturbations of a charged four dimensional
stringy black hole arising from gauging a previously studied WZW model. We find
that the black hole is stable only in the extremal case $Q=M$.
|
hep-th/9204032
| 727,301 |
If the electroweak symmetry breaking sector contains colored particles
weighing a few hundred GeV, then they will be copiously produced at a hadron
supercollider. Colored technipions can rescatter into pairs of gauge bosons. As
proposed by Bagger, Dawson, and Valencia, this leads to gauge boson pair rates
far larger than in the standard model. In this note we reconsider this
mechanism, and illustrate it in a model in which the rates can be reliably
calculated. The observation of both an enhanced rate of gauge-boson-pair events
and colored particles would be a signal that the colored particles were
pseudo-Goldstone bosons of symmetry breaking.
|
hep-ph/9204220
| 727,301 |
We study the Quantum Field Theory of nonrelativistic bosons coupled to a
Chern--Simons gauge field at nonzero particle density. This field theory is
relevant to the study of anyon superconductors in which the anyons are
described as {\bf bosons} with a statistical interaction. We show that it is
possible to find a mean field solution to the equations of motion for this
system which has some of the features of bose condensation. The mean field
solution consists of a lattice of vortices each carrying a single quantum of
statistical magnetic flux. We speculate on the effects of the quantum
corrections to this mean field solution. We argue that the mean field solution
is only stable under quantum corrections if the Chern--Simons coefficient
$N=2\pi\theta/g^2$ is an integer. Consequences for anyon superconductivity are
presented. A simple explanation for the Meissner effect in this system is
discussed.
|
hep-th/9204033
| 727,301 |
We performed detailed study of the phase transition region in Four
Dimensional Simplicial Quantum Gravity, using the dynamical triangulation
approach. The phase transition between the Gravity and
Antigravity phases turned out to be asymmetrical, so that we observed the
scaling laws only when the Newton constant approached the critical value from
perturbative side. The curvature susceptibility diverges with the scaling index
$-.6$. The physical (i.e. measured with heavy particle propagation) Hausdorff
dimension of the manifolds, which is
2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4
at the critical point, within the measurement accuracy. These facts indicate
the existence of the continuum limit in Four
Dimensional Euclidean Quantum Gravity.
|
hep-lat/9204004
| 727,301 |
We investigate pairing instabilities in the Fermi-liquid-like state of a
single species of anyons. We describe the anyons as Fermions interacting with a
Chern-Simons gauge field and consider the weak coupling limit where their
statistics approaches that of Fermions. We show that, within the conventional
BCS approach, due to induced repulsive Coulomb and current-current
interactions, the attractive Aharonov-Bohm interaction is not sufficient to
generate a gap in the Fermion spectrum.
|
cond-mat/9204005
| 727,301 |
$QCD$ renormalization for the top-quark mass is calculated in a mass
geometrical mean hierarchy, $m_d m_b = m_s^2$ and $m_u m_t = m_c^2$. The
physical mass, $m_t(m_t) = 160 {\pm} 50 GeV$ is obtained, which agrees very
well with electroweak precision measurement.
|
hep-ph/9204221
| 727,301 |
An investigation is made of the super-Calogero model with particular emphasis
on its continuum formulation and possible application in the context of
supersymmetrizing the bosonic collective d=1 string field theory.
|
hep-th/9204034
| 727,302 |
We calculate the cross-section for events at HERA where the proton loses only
a minute fraction of its initial energy, all of which goes into producing a
single pair of transverse jets.
|
hep-ph/9204222
| 727,302 |
We study the effect of introducing a weak antiferromagnetic interplanar
exchange coupling in the two dimensional frustrated Heisenberg model. We show
that a ferromagnetic(FM) ordering of chirality - {\it i.e.}, same chirality on
adjacent planes - is energetically favoured, thus leading to bulk violation of
the discrete symmetries parity($P$) and time reversal($T$).
|
cond-mat/9204006
| 727,302 |
We give an integrable extension of the lattice models recently considered by
I.Kostov in his study of strings in discrete space. These models are IRF models
with spin variables living in any connected graph, the vertex model underlying
these models is the Izergin-Korepin model. When the graph is taken to be a
simply laced Dynkin diagram, it is conjectured that these models possess
critical regimes which are the dilute phase of SOS models of ADE type.
|
hep-th/9204036
| 727,302 |
The three point correlation functions with twist fields are determined for
bosonic $Z_N$ orbifolds. Both the choice of the modular background (compatible
with the twist) and of the (higher) twisted sectors involved are fully general.
We point out a necessary restriction on the set of instantons contributing to
twist field correlation functions not obtained in previous calculations. Our
results show that the theory is target space duality invariant.
|
hep-th/9204037
| 727,302 |
We develop a theory of polymers in a nematic solvent by exploiting an analogy
with two-dimensional quantum bosons at zero temperature. We argue that the
theory should also describe polymers in an {\sl isotropic} solvent. The dense
phase is analyzed in a Bogoliubov-like approximation, which assumes a broken
symmetry in the phase of the boson order parameter. We find a stiffening of the
longitudinal fluctuations of the nematic field, calculate the density-density
correlation function, and extend the analysis to the case of ferro- and
electrorheological fluids. The boson formalism is used to derive a simple
hydrodynamic theory which is indistinguishable from the corresponding theory of
polymer nematics in an isotropic solvent at long wavelengths. We also use
hydrodynamics to discuss the physical meaning of the boson order parameter. A
renormalization group treatment in the dilute limit shows that logarithmic
corrections to polymer wandering, predicted by de Gennes, are unaffected by
interpolymer interactions. A continuously variable Flory exponent appears for
polymers embedded in a {\sl two}-dimensional nematic solvent. We include free
polymer ends and hairpin configurations in the theory and show that hairpins
are described by an Ising-like symmetry-breaking term in the boson field
theory.
|
cond-mat/9204007
| 727,302 |
It has been known for some time that $W$ algebras can be realised in terms of
an energy-momentum tensor together with additional free scalar fields. Some
recent results have shown that more general realisations are also possible. In
this paper, we consider a wide class of realisations that may be obtained from
the Miura transformation, related to the existence of canonical subalgebras of
the Lie algebras on which the $W$ algebras are based. We give explicit formulae
for all realisations of this kind, and discuss their applications in $W$-string
theory.
|
hep-th/9204038
| 727,302 |
It is proved that for a symmetric convex body K in R^n, if for some tau > 0,
|K cap (x+tau K)| depends on ||x||_K only, then K is an ellipsoid. As a part of
the proof, smoothness properties of convolution bodies ls are studied.
|
math/9204212
| 727,302 |
Gives a short proof of Dehornoy's latest result. The same simple argument
(and more) was discovered by Laver's student Larue.
|
math/9204206
| 727,303 |
A very short proof of G\"odel's second incompleteness theorem (for set
theory, second order arithmetic etc.)
|
math/9204207
| 727,303 |
A stationary subset S of a regular uncountable cardinal kappa reflects fully
at regular cardinals if for every stationary set T subseteq kappa of higher
order consisting of regular cardinals there exists an alpha in T such that S
cap alpha is a stationary subset of alpha. We prove that the Axiom of Full
Reflection which states that every stationary set reflects fully at regular
cardinals, together with the existence of n-Mahlo cardinals is equiconsistent
with the existence of Pi^1_n-indescribable cardinals. We also state the
appropriate generalization for greatly Mahlo cardinals.
|
math/9204218
| 727,303 |
The connections between Whitehead groups and uniformization properties were
investigated by the third author in [Sh:98]. In particular it was essentially
shown there that there is a non-free Whitehead (respectively,
aleph_1-coseparable) group of cardinality aleph_1 if and only if there is a
ladder system on a stationary subset of omega_1 which satisfies
2-uniformization (respectively, omega-uniformization). These techniques allowed
also the proof of various independence and consistency results about Whitehead
groups, for example that it is consistent that there is a non-free Whitehead
group of cardinality aleph_1 but no non-free aleph_1-coseparable group.
However, some natural questions remained open, among them the following two:
(i) Is it consistent that the class of W-groups of cardinality aleph_1 is
exactly the class of strongly aleph_1-free groups of cardinality aleph_1 ? (ii)
If every strongly aleph_1-free group of cardinality aleph_1 is a W-group, are
they also all aleph_1-coseparable? In this paper we use the techniques of
uniformization to answer the first question in the negative and give a partial
affirmative answer to the second question.
|
math/9204219
| 727,303 |
We investigate the system of holomorphic differential identities implied by
special K\"ahlerian geometry of four-dimensional N=2 supergravity. For
superstring compactifications on \cy threefolds these identities are equivalent
to the Picard-Fuchs equations of algebraic geometry that are obeyed by the
periods of the holomorphic three-form. For one variable they reduce to linear
fourth-order equations which are characterized by classical $W$-generators; we
find that the instanton corrections to the Yukawa couplings are directly
related to the non-vanishing of $w_4$. We also show that the symplectic
structure of special geometry can be related to the fact that the Yukawa
couplings can be written as triple derivatives of some holomorphic function
$F$. Moreover, we give the precise relationship of the Yukawa couplings of
special geometry with three-point functions in topological field theory.
|
hep-th/9204035
| 727,303 |
We suggest a model of induced gravity in which the fundamental object is a
relativistic {\it membrane} minimally coupled to a background metric and to an
external three index gauge potential. We compute the low energy limit of the
two-loop effective action as a power expansion in the surface tension. A
generalized bootstrap hypothesis is made in order to identify the physical
metric and gauge field with the lowest order terms in the expansion of the
vacuum average of the composite operators conjugate to the background fields.
We find that the large distance behaviour of these classical fields is
described by the Einstein action with a cosmological term plus a Maxwell type
action for the gauge potential. The Maxwell term enables us to apply the
Hawking-Baum argument to show that the physical cosmological constant is
``~probably~'' zero.
|
hep-th/9204039
| 727,303 |
We consider the solutions of the field equations for the large $N$ dilaton
gravity model in $1+1$ dimensions recently proposed by Callan, Giddings, Harvey
and Strominger (CGHS). We find time dependant solutions with finite mass and
vanishing flux in the weak coupling regime, as well as solutions which lie
entirely in the Liouville region.
|
hep-th/9204042
| 727,303 |
We study the twisted version of the supersymmetric
$G/T=SU(n)/U(1)^{\otimes(n-1)} gauged Wess-Zumino-Witten model. By studying its
fixed points under BRST transformation this model is shown to be reduced to a
simple topological field theory, that is, the topological matter system in the
K.Li's theory of 2 dimensional gravity for the case of $n=2$, and its
generalization for $n \geq 3$.
|
hep-th/9204043
| 727,303 |
Perturbation theory for a class of topological field theories containing
antisymmetric tensor fields is considered. These models are characterized by a
supersymmetric structure which allows to establish their perturbative
finiteness.
|
hep-th/9204044
| 727,303 |
We analyze an abelian gauge model in 3 dimensions which includes massless
scalar matter fields. By controlling the trace anomalies with a local
dilatation Ward identity, we show that, in perturbation theory and within the
BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies,
in particular, the vanishing of the corresponding $\beta$ function in the
renormalization group equation.
|
hep-th/9204045
| 727,303 |
We show that the strong coupling limit of d-dimensional quantum
electrodynamics with $2^{d}/2^{[d/2]}$ flavors of fermions can be mapped onto
the s=1/2 quantum Heisenberg antiferromagnet in d-1 space dimensions. The
staggered N\'eel order parameter is the expectation value of a mass operator in
QED and the spin-waves are pions. We speculate that the chiral symmetry
breaking phase transition corresponds to a transition between the flux phase
and the conventional N\'eel ordered phase of an antiferromagnetic t-J model.
|
hep-th/9204047
| 727,303 |
We construct a solution of the classical equations of motion arising in the
low energy effective field theory for heterotic string theory. This solution
describes a black hole in four dimensions carrying mass $M$, charge $Q$ and
angular momentum $J$. The extremal limit of the solution is discussed.
|
hep-th/9204046
| 727,303 |
The purpose of this note is to prove irreflexivity, and hence the linear
ordering, in ZFC, without some of the machinery used by Dehornoy.
|
math/9204208
| 727,304 |
We show that it is possible to formulate Abelian Chern-Simons theory on a
lattice as a topological field theory. We discuss the relationship between
gauge invariance of the Chern-Simons lattice action and the topological
interpretation of the canonical structure. We show that these theories are
exactly solvable and have the same degrees of freedom as the analogous
continuum theories.
|
hep-th/9204048
| 727,304 |
The ground ring structure of 1+1 dimensional string theory leads to an
infinite set of non linear recursion relations among the `bulk' scattering
amplitudes of open and closed tachyons on the disk, which fix them uniquely.
The relations are generated by the action of the ring on the tachyon modules;
associativity of this action determines all structure constants. This algebraic
structure may allow one to relate the continuum picture to a matrix model.
|
hep-th/9204049
| 727,304 |
We calculate gravitational dressed tachyon correlators in non critcal
dimensions. The 2D gravity part of our theory is constrained to constant
curvature. Then scaling dimensions of gravitational dressed vertex operators
are equal to their bare conformal dimensions. Considering the model as d+2
dimensional critical string we calculate poles of generalized Shapiro-Virasoro
amplitudes.
|
hep-th/9204051
| 727,304 |
I propose a numerical simulation algorithm for statistical systems which
combines a microcanonical transfer of energy with global changes in clusters of
spins. The advantages of the cluster approach near a critical point augment the
speed increases associated with multi-spin coding in the microcanonical
approach. The method also provides a limited ability to tune the average
cluster size.
|
hep-lat/9204005
| 727,304 |
We rederive the $w_\infty$ Ward identities, starting from the existence of
trivial linearized gauge invariances, and using the method of canceled
propagators in the operator formalism. Recursion relations for certain classes
of correlation functions are derived, and these correlation function are
calculated exactly. We clarify the relation of these results with another
derivation of the Ward identities, which relies directly on charge
conservation. We also emphasize the importance of the kinematics of canceled
propagators in ensuring that the Ward identities are non-trivial. Finally, we
sketch an extension of Ward identities to open strings.
|
hep-th/9204052
| 727,304 |
The matrix element which determines the B meson decay constant can be
measured on the lattice using an effective field theory for heavy quarks.
Various discretizations of the heavy-light bilinears which appear in this and
other B decay matrix elements are possible. The heavy-light bilinear currently
used for the determination of the B meson decay constant on the lattice suffers
a substantial one-loop renormalization. In this paper, we compute the one-loop
renormalizations of the discretizations in which the heavy and light fields in
the bilinear are separated by one lattice spacing, and discuss their
application. Readers of this paper may also be interested in our paper on the
application of Symanzik's improvement program to heavy-light currents (paper
number 9203221 on hep-ph).
|
hep-lat/9204006
| 727,304 |
This paper, dating from May 1991, contains preliminary (and unpublishable)
notes on investigations about iteration trees. They will be of interest only to
the specialist.
In the first two sections I define notions of support and embeddings for tree
iterations, proving for example that every tree iteration is a direct limit of
finite tree iterations. This is a generalization to models with extenders of
basic ideas of iterated ultrapowers using only ultrapowers.
In the final section (which is most of the paper) I sketch a proof that any
tree iteration can be embedded into a normal iteration, that is, a tree
iteration with the extenders in nondecreasing order of strength and with
strictly increasing critical points.
|
math/9204209
| 727,305 |
We study the contribution of finite energy tunneling to the total vacuum
transition rate in a system at finite temperature. We find that in certain
models, such as the 1+1 Abelian Higgs model, the quantum contribution is
non-negligible even at large temperatures. We show how the persistence of the
cosmological baryon asymmetry yields a bound on the inclusive two particle
cross section in the anomalous (B violating) sector.
|
hep-ph/9204223
| 727,305 |
The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in
terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show
that the magnon excitations and the s=1/2, n-magnon bound states are determined
by the algebra. Thus the Gamma_q(1) symmetry provides a description that
naturally induces the Bethe Ansatz. The recurrence relations determined by
Gamma_q(1) permit to express the energy of the n-magnon bound states in a
closed form in terms of Tchebischeff polynomials.
|
hep-th/9204054
| 727,305 |
Parametrized field theories, which are generally covariant versions of
ordinary field theories, are studied from the point of view of the covariant
phase space: the space of solutions of the field equations equipped with a
canonical (pre)symplectic structure. Motivated by issues arising in general
relativity, we focus on: phase space representations of the spacetime
diffeomorphism group, construction of observables, and the relationship between
the canonical and covariant phase spaces.
|
hep-th/9204055
| 727,305 |
The two-dimensional self-dual Chern--Simons equations are equivalent to the
conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged
nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In
this paper we classify all finite charge $SU(N)$ solutions by first
transforming the self-dual Chern--Simons equations into the two-dimensional
chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood
classification of harmonic maps into the unitary groups. This construction also
leads to a new relationship between the $SU(N)$ Toda and $SU(N)$ chiral model
solutions.
|
hep-th/9204056
| 727,305 |
An elementary derivation is given for the ``Peierles substitution'' used in
projecting dynamics in a strong magnetic field onto the lowest Landau level.
The projection of wavefunctions and the ordering prescription for the projected
Hamiltonian is explained.
|
hep-th/9204057
| 727,305 |
Consider $d$ disjoint closed subintervals of the unit interval and consider
an orientation preserving expanding map which maps each of these subintervals
to the whole unit interval. The set of points where all iterates of this
expanding map are defined is a Cantor set. Associated to the construction of
this Cantor set is the scaling function which records the infinitely deep
geometry of this Cantor set. This scaling function is an invariant of $C^1$
conjugation. We solve the inverse problem posed by Dennis Sullivan: given a
scaling function, determine the maximal possible smoothness of any expanding
map which produces it.
|
math/9204241
| 727,308 |
We investigate a class of (2,2) supersymmetric string vacua which may be
represented as Landau--Ginzburg theories with a quasihomogeneous potential
which has an isolated singularity at the origin. There are at least three
thousand distinct models in this class. All vacua of this type lead to Euler
numbers which lie in the range $-960 \leq \chi \leq 960$. The Euler
characteristics do not pair up completely hence the space of Landau--Ginzburg
ground states is not mirror symmetric even though it exhibits a high degree of
symmetry. We discuss in some detail the relation between Landau--Ginzburg
models and Calabi--Yau manifolds and describe a subtlety regarding
Landau--Ginzburg potentials with an arbitrary number of fields. We also show
that the use of topological identities makes it possible to relate
Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual
Landau-Ginzburg framework does not apply.
|
hep-th/9204060
| 727,308 |
A field theoretic formulation of the Marinari-Parisi supersymmetric matrix
model is established and shown to be equivalent to a recently proposed
supersymmetrization of the bosonic collective string field theory. It also
corresponds to a continuum description of super-Calogero models. The
perturbation theory of the model is developed and, in this approach, an
infinite sequence of vertices is generated. A class of potentials is identified
for which the spectrum is that of a massless boson and Majorana fermion. For
the harmonic oscillator case, the cubic vertices are obtained in an oscillator
basis. For a rather general class of potentials it is argued that one cannot
generate from Marinari-Parisi models a continuum limit similar to that of the
d=1 bosonic string.
|
hep-th/9204061
| 727,308 |
It has recently become fashionable to regard black holes as elementary
particles. By taking this suggestion seriously it is possible to cobble
together an elementary particle physics based estimate for the decay rate
$(\hbox{black hole})_i \to (\hbox{black hole})_f + (\hbox{massless quantum})$.
This estimate of the spontaneous emission rate contains two free parameters
which may be fixed by demanding that the high energy end of the spectrum of
emitted quanta match a blackbody spectrum at the Hawking temperature. The
calculation, though technically trivial, has important conceptual implications:
(1) The existence of Hawking radiation from black holes is ultimately dependent
only on the fact that massless quanta (and all other forms of matter) couple to
gravity. (2) The thermal nature of the Hawking spectrum depends only on the
fact that the number of internal states of a large mass black hole is enormous.
(3) Remarkably, the resulting formula for the decay rate gives meaningful
answers even when extrapolated to low mass black holes. The analysis strongly
supports the scenario of complete evaporation as the endpoint of the Hawking
radiation process (no naked singularity, no stable massive remnant).
|
hep-th/9204062
| 727,308 |
We solve Virasoro constraints on the KP hierarchy in terms of minimal
conformal models. The constraints we start with are implemented by the Virasoro
generators depending on a background charge $Q$. Then the solutions to the
constraints are given by the theory which has the same field content as the
David-Distler-Kawai theory: it consists of a minimal matter scalar with
background charge $Q$, dressed with an extra `Liouville' scalar. The
construction is based on a generalization of the Kontsevich parametrization of
the KP times achieved by introducing into it Miwa parameters which depend on
the value of $Q$. Under the thus defined Kontsevich-Miwa transformation, the
Virasoro constraints are proven to be equivalent to a master equation depending
on the parameter $Q$. The master equation is further identified with a
null-vector decoupling equation. We conjecture that $W^{(n)}$ constraints on
the KP hierarchy are similarly related to a level-$n$ decoupling equation. We
also consider the master equation for the $N$-reduced KP hierarchies. Several
comments are made on a possible relation of the generalized master equation to
{\it scaled} Kontsevich-type matrix integrals and on the form the equation
takes in higher genera.
|
hep-th/9204063
| 727,308 |
We present an analysis of hadronic spectroscopy for Wilson valence quarks
with dynamical staggered fermions at lattice coupling $6/g^2 = \beta=5.6$ at
sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched
approximation at $\beta=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We
make comparisons with our previous results with dynamical staggered fermions at
the same parameter values but on $16^4$ lattices doubled in the temporal
direction.
|
hep-lat/9204008
| 727,309 |
Motivated by some previous work on fermions on random lattices and by
suggestions that impurities could trigger parity breaking in 2d crystals, we
have analyzed the spectrum of the Dirac equation on a two dimensional square
lattice where sites have been removed randomly --- a doped lattice. We have
found that the system is well described by a sine-Gordon action. The solitons
of this model are the lattice fermions, which pick a quartic interaction due to
the doping and become Thirring fermions. They also get an effective mass
different from the lagrangian mass. The system seems to exhibit spontaneous
symmetry breaking, exactly as it happens for a randomly triangulated lattice.
The associated ``Goldstone boson" is the sine-Gordon scalar. We argue, however,
that the peculiar behaviour of the chiral condensate is due to finite size
effects.
|
hep-lat/9204009
| 727,309 |
In theories where spacetime is a direct product of Minkowski space ($M^4$)
and a d dimensional compact space ($K^d$), there can exist topological solitons
that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the
compact dimensions. A paradigmatic non-gravitational example of such
``co-winding" solitons is furnished by Yang-Mills theory defined on $M^4 X
S^1$. Pointlike, stringlike and sheetlike solitons can be identified by
transcribing and generalizing the proceedure used to construct the periodic
instanton (caloron) solutions. Asymptotically the classical pointlike objects
have non-Abelian magnetic dipole fields together with a non-Abelian scalar
potential while the ``color" electric charge is zero. However quantization of
collective coordinates associated with zeromodes and coupling to fermions can
radically change these quantum numbers due to fermion number fractionalization
and its non-Abelian generalization. Interpreting the YM group as color (or the
Electroweak SU(2) group) and assuming that an extra circular dimension exists
thus implies the existence of topologically stable solitonic objects which
carry baryon(lepton) number and a mass O($1/g^2R$), where R is the radius of
the compact dimension.
|
hep-th/9204066
| 727,309 |
An extension of the Field-Antifield formalism to treat anomalous gauge
theories with a closed, irreducible classical gauge algebra is proposed.
Introducing extra degrees of freedom, we construct the gauge transformations
for these new fields, the Wess-Zumino term and the corresponding measure.
|
hep-th/9204065
| 727,309 |
A delicate interplay between the anomalous magnetic moments of the proton and
neutron makes, in magnetic fields $B\ge 2\times 10^{14}$ T, the neutron stable
and for fields $B\ge 5\times 10^{14}$ T the proton becomes unstable to a decay
into a neutron via $\beta$ emission. Limits on the field strengths for which
these arguments hold are presented and are related to questions of vacuum
stability in the presence of such fields. Possible astrophysical consequences
are discussed.
|
hep-ph/9204224
| 727,309 |
We present a new method of determining the anisotropy of the gap function in
layered high-Tc superconductors. Careful inelastic neutron scattering
measurements at low temperature of the phonon dispersion curves in the (100)
direction in La_(1.85)Sr_(.15)CuO_4 would determine whether the gap is
predominately s-wave or d-wave. We also propose an experiment to determine the
gap at each point on a quasi-two-dimensional Fermi surface.
|
cond-mat/9204008
| 727,309 |
We prove that Hilbert space is distortable and, in fact, arbitrarily
distortable. This means that for all lambda >1 there exists an equivalent norm
|.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there
exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|.
We also prove that if X is any infinite dimensional Banach space with an
unconditional basis then the unit sphere of X and the unit sphere of l_1 are
uniformly homeomorphic if and only if X does not contain l_infty^n's uniformly.
|
math/9204213
| 727,309 |
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the
thermodynamic limit, where the model becomes invariant under the action of
affine U_q( sl(2) ).
Our method is based on the representation theory of quantum affine algebras,
the related vertex operators and KZ equation, and thereby bypasses the usual
process of starting from a finite lattice, taking the thermodynamic limit and
filling the Dirac sea. From recent results on the algebraic structure of the
corner transfer matrix of the model, we obtain the vacuum vector of the
Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex
operators, which act as particle creation operators in the space of
eigenvectors.
We check the agreement of our results with those obtained using the Bethe
Ansatz in a number of cases, and with others obtained in the scaling limit ---
the $su(2)$-invariant Thirring model.
|
hep-th/9204064
| 727,310 |
We generalize the Lax pair and B\"acklund transformations for Toda and N=1
super Toda equations to the case of arbitrary worldsheet background geometry.
We use the fact that the Toda equations express constant curvature conditions,
which arise naturally from flatness conditions equivalent to the W--gravity
equations of motion.
|
hep-th/9204067
| 727,310 |
A generally covariant gauge theory for an arbitrary gauge group with
dimension $\geq 3$, that reduces to Ashtekar's canonical formulation of gravity
for SO(3,C), is presented. The canonical form of the theory is shown to contain
only first class constraints.
|
hep-th/9204069
| 727,310 |
We investigate the influence of the measure in the path integral for
Euclidean quantum gravity in four dimensions within the Regge calculus. The
action is bounded without additional terms by fixing the average lattice
spacing. We set the length scale by a parameter $\beta$ and consider a scale
invariant and a uniform measure. In the low $\beta$ region we observe a phase
with negative curvature and a homogeneous distribution of the link lengths
independent of the measure. The large $\beta$ region is characterized by
inhomogeneous link lengths distributions with spikes and positive curvature
depending on the measure.
|
hep-lat/9204010
| 727,310 |
A chromoelectric vacuum that confines both gluon and quark degrees of freedom
(in the sense that they do not exist as asymptotic states) is constructed.
However some degrees of freedom still exist as asymptotic states thereby
allowing colour singlets to propagate.
|
hep-ph/9204230
| 727,310 |
Sea quark contributions to the scalar density and the axial current matrix
elements of the nucleon are studied in lattice qcd with two flavours of
dynamical wilson fermions. the results are compared to trends in heavy quark
mass expansions, and contrasted with the numbers obtained using dynamical
staggered fermions.
|
hep-lat/9204012
| 727,310 |
We construct a manifestly $N=(4,0)$ world-sheet supersymmetric twistor-like
formulation of the $D=6$ Green-Schwarz superstring, using the principle of
double (target-space and world-sheet) Grassmann analyticity. The superstring
action contains two Lagrange multiplier terms and a Wess-Zumino term. They are
written down in the analytic subspace of the world-sheet harmonic $N=(4,0)$
superspace, the target manifold being too an analytic subspace of the harmonic
$D=6\;\; N=1$ superspace. The kappa symmetry of the $D=6$ superstring is
identified with a Kac-Moody extension of the world-sheet $N=(4,0)$
superconformal symmetry. It can be enlarged to include the whole world-sheet
reparametrization group if one introduces the appropriate gauge Beltrami
superfield into the action. To illustrate the basic features of the new $D=6$
superstring construction, we first give some details about the simpler (already
known) twistor-like formulations of $D=3, N=(1,0)$ and $D=4, N=(2,0)$
superstrings.
|
hep-th/9204071
| 727,310 |
Using renormalization group techniques, we examine several interesting
relations among masses and mixing angles of quarks and leptons in the Standard
Model. We extend the analysis to the minimal supersymmetric extension to
determine its effect on these mass relations. Remarkably Supersymmetry allows
for these relations to be satisfied at a single grand unified scale.
|
hep-ph/9204225
| 727,310 |
A method of constructing an entire function with given zeros and estimates of
growth is suggested. It gives a possibility to describe zero sets of certain
classes of entire functions of one and several variables in terms of growth of
volume of these sets in certain polycylinders.
|
math/9204201
| 727,310 |
We study the effects of virtual leptoquarks on charged current and neutral
current processes at the $ep$ collider HERA. We present the areas of parameter
space that can be excluded at HERA by searching for deviations from Standard
Model expectations. The best results are obtained by examining the ratio of
neutral current to charged current cross sections, $R=\sigma_{NC}/\sigma_{CC}$,
where, with $200\inpb$ of integrated luminosity for unpolarized $e^-$ and $e^+$
beams, HERA can search for leptoquarks with masses up to $\sim 800\gev$, with
leptoquark coupling strengths of order $\alpha_{em}$.
|
hep-ph/9204226
| 727,310 |
We investigate the use of two types of non-local (``smeared'') sources for
quark propagators in quenched lattice QCD at $\beta=6.0$ using Wilson fermions
at $\kappa=0.154$ and $0.155$. We present results for the hadron mass spectrum,
meson decay constants, quark masses, the chiral condensate and the quark
distribution amplitude of the pion. The use of smeared sources leads to a
considerable improvement over previous results. We find a disturbing
discrepancy between the baryon spectra obtained using Wuppertal and wall
sources. We find good signals in the ratio of correlators used to calculate the
quark mass and the chiral condensate and show that the extrapolation to the
chiral limit is smooth.
|
hep-lat/9204011
| 727,310 |
A subset $A$ of a Boolean algebra $B$ is said to be $(n,m)$-reaped if there
is a partition of unity $P \subset B$ of size $n$ such that the cardinality of
$\{b \in P: b \wedge a \neq \emptyset\}$ is greater than or equal to $m$ for
all $a\in A$. The reaping number $r_{n,m}(B)$ of a Boolean algebra $B$ is the
minimum cardinality of a set $A \subset B\setminus \{0\}$ such which cannot be
$(n,m)$-reaped. It is shown that, for each $n \in \omega$, there is a Boolean
algebra $B$ such that $r_{n+1,2}(B) \neq r_{n,2}(B)$. Also, $\{r_{n,m}(B) :
\{n,m\}\subseteq\omega\}$ consists of at most two consecutive integers. The
existence of a Boolean algebra $B$ such that $r_{n,m}(B) \neq r_{n',m'}(B)$ is
equivalent to a statement in finite combinatorics which is also discussed.
|
math/9204210
| 727,311 |
Broken gauge symmetries are typically restored at high temperature, and the
leading-order result for the critical temperature $T_c$ was found many years
ago by Weinberg and by Dolan and Jackiw. I find a simple expression for the
next-to-leading order correction to $T_c$, which is order $e T_c$ where $e$ is
the gauge coupling. The result is a simple consequence of recent work on
summing ring diagrams at high temperature in gauge theories. The result is
valid when the Higgs self-coupling $\lambda$ is the same order as $e^2$, and it
does not address the case of strongly first-order phase transitions, which
arise when $\lambda \ll e^2$.
|
hep-ph/9204228
| 727,311 |
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