78 research outputs found
Universality and the magnetic catalysis of chiral symmetry breaking
The hypothesis that the magnetic catalysis of chiral symmetry breaking is due
to interactions of massless fermions in their lowest Landau level is examined
in the context of chirally symmetric models with short ranged interactions. It
is argued that, when the magnetic field is sufficiently large, even an
infinitesimal attractive interaction in the appropriate channel will break
chiral symmetry.Comment: 24 pages, 6 figures, REVTeX. The final version with minor
corrections. To appear in Phys Rev D60 (1999
Intersections forms and the geometry of lattice Chern-Simons theory
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.Comment: 14 page
Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory
Correlators of Wilson loop operators with O_4=Tr(F_{\mu\nu}^2+...) are
computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The
results are compared with the leading order perturbative computations. As a
consequence of conformal invariance, these correlators have identical forms in
the weak and strong coupling limits for circular loops. They are essentially
different for contours not protected by conformal symmetry.Comment: 7 pages, 1 postscript figure, minor corrections and clarifying
argument
Thermodynamics of D0-branes in matrix theory
We examine the matrix theory representation of D0-brane dynamics at finite
temperature. In this case, violation of supersymmetry by temperature leads to a
non-trivial static potential between D0-branes at any finite temperature. We
compute the static potential in the 1-loop approximation and show that it is
short-ranged and attractive. We compare the result with the computations in
superstring theory. We show that thermal states of D0-branes can be reproduced
by matrix theory only when certain care is taken in integration over the moduli
space of classical solutions in compactified time.Comment: 13 pages, 1 figur
Deconfinement Transition for Quarks on a Line
We examine the statistical mechanics of a 1-dimensional gas of both adjoint
and fundamental representation quarks which interact with each other through
1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when
the density of fundamental quarks is small, there is a first order phase
transition at a critical temperature and adjoint quark density which can be
interpreted as deconfinement. When the fundamental quark density is comparable
to the adjoint quark density, the phase transition becomes a third order one.
We formulate a way to distinguish the phases by considering the expectation
values of high winding number Polyakov loop operators.Comment: Reported problems with figures fixed; 38 pages, LaTeX, 5 figures,
epsfi
Driving Operators Relevant: A Feature of Chern-Simons Interaction
By computing anomalous dimensions of gauge invariant composite operators
and in Chern-Simons fermion and boson
models, we address that Chern-Simons interactions make these operators more
relevant or less irrelevant in the low energy region. We obtain a critical
Chern-Simons fermion coupling, , for a phase
transition at which the leading irrelevant four-fermion operator
becomes marginal, and a critical Chern-Simons boson
coupling, , for a similar phase transition
for the leading irrelevant operator . We see this phenomenon
also in the expansion.Comment: (ten pages, latex, figures included
Loop Correlators and Theta States in 2D Yang-Mills Theory
Explicit computations of the partition function and correlation functions of
Wilson and Polyakov loop operators in theta-sectors of two dimensional
Yang-Mills theory on the line cylinder and torus are presented. Several
observations about the correspondence of two dimensional Yang-Mills theory with
unitary matrix quantum mechanics are presented. The incorporation of the
theta-angle which characterizes the states of two dimensional adjoint QCD is
discussed.Comment: 30 pages, Latex, no figure
Area Law and Continuum Limit in "Induced QCD"
We investigate a class of operators with non-vanishing averages in a
D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the
operators considered are ``filled Wilson loops" which are the most reasonable
counterparts of Wilson loops in the conventional Wilson formulation of lattice
QCD. The averages of interest are represented as partition functions of certain
2-dimensional statistical systems with nearest neighbor interactions. The
``string tension" , which is the exponent in the area law for the
``filled Wilson loop" is equal to the free energy density of the corresponding
statistical system. The continuum limit of the Kazakov--Migdal model
corresponds to the critical point of this statistical system. We argue that in
the large limit this critical point occurs at zero temperature. In this
case we express in terms of the distribution density of eigenvalues
of the matrix-valued master field. We show that the properties of the continuum
limit and the description of how this limit is approached is very unusual and
differs drastically from what occurs in both the Wilson theory () and in the ``adjoint'' theory (). Instead, the continuum limit of the model appears to be
intriguingly similar to a string theory.Comment: 38 page
Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
Perturbative computations of the expectation value of the Wilson loop in N=4
supersymmetric Yang-Mills theory are reported. For the two special cases of a
circular loop and a pair of anti-parallel lines, it is shown that the sum of an
infinite class of ladder-like planar diagrams, when extrapolated to strong
coupling, produces an expectation value characteristic of the results of the
AdS/CFT correspondence, . For the case of
the circular loop, the sum is obtained analytically for all values of the
coupling. In this case, the constant factor in front of also
agrees with the supergravity results. We speculate that the sum of diagrams
without internal vertices is exact and support this conjecture by showing that
the leading corrections to the ladder diagrams cancel identically in four
dimensions. We also show that, for arbitrary smooth loops, the ultraviolet
divergences cancel to order .Comment: 24 pages, LaTeX, uses feynmp, 12 postscript figure
SU(N) Antiferromagnets and Strongly Coupled QED: Effective Field Theory for Josephson Junctions Arrays
We review our analysis of the strong coupling of compact QED on a lattice
with staggered Fermions. We show that, for infinite coupling, compact QED is
exactly mapped in a quantum antiferromagnet. We discuss some aspects of this
correspondence relevant for effective field theories of Josephson junctions
arrays.Comment: 33 pages,latex,Proceedings of "Common Trends in Condensed Matter and
High Energy Physics",DFUPG 1/9
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