1,272 research outputs found
QCD Dirac Spectra With and Without Random Matrix Theory
Recent work on the spectrum of the Euclidean Dirac operator spectrum show
that the exact microscopic spectral density can be computed in both random
matrix theory, and directly from field theory. Exact relations to effective
Lagrangians with additional quark species form the bridge between the two
formulations. Taken together with explicit computations in the chGUE random
matrix ensemble, a series of universality theorems are used to prove that the
finite-volume QCD partition function coincides exactly with the universal
double-microscopic limit of chUE random matrix partition functions. In the
limit where N_f and N_c both go to infinity with the ratio N_f/N_c fixed, the
relevant effective Lagrangian undergoes a third order phase transition of
Gross-Witten type.Comment: LaTeX, 6 page
Quenched and Unquenched Chiral Perturbation Theory in the \epsilon-Regime
The chiral limit of finite-volume QCD is the -regime of the theory.
We discuss how this regime can be used for determining low-energy observables
of QCD by means of comparisons between lattice simulations and quenched and
unquenched chiral perturbation theory. The quenched theory suffers in the
-regime from ``quenched finite volume logs'', the finite-volume
analogs of quenched chiral logs.Comment: LaTeX, 7 pages, contribution to LHP200
Dirac Operator Spectra from Finite-Volume Partition Functions
Based on the relation to random matrix theory, exact expressions for all
microscopic spectral correlators of the Dirac operator can be computed from
finite-volume partition functions. This is illustrated for the case of
gauge theories with and fermions in the fundamental
representation.Comment: LaTeX, 6 page
Partition Function Zeros of an Ising Spin Glass
We study the pattern of zeros emerging from exact partition function
evaluations of Ising spin glasses on conventional finite lattices of varying
sizes. A large number of random bond configurations are probed in the framework
of quenched averages. This study is motivated by the relationship between
hierarchical lattice models whose partition function zeros fall on Julia sets
and chaotic renormalization flows in such models with frustration, and by the
possible connection of the latter with spin glass behaviour. In any finite
volume, the simultaneous distribution of the zeros of all partition functions
can be viewed as part of the more general problem of finding the location of
all the zeros of a certain class of random polynomials with positive integer
coefficients. Some aspects of this problem have been studied in various
branches of mathematics, and we show how polynomial mappings which are used in
graph theory to classify graphs, may help in characterizing the distribution of
zeros. We finally discuss the possible limiting set as the volume is sent to
infinity.Comment: LaTeX, 18 pages, hardcopies of 15 figures by request to
[email protected], CERN--TH-7383/94 (a note and a reference added
The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories
We confront Cardy's suggested c-function for four-dimensional field theories
with the spontaneous breaking of chiral symmetries in asymptotically free
vectorlike gauge theories with fermions transforming according to different
representations under the gauge group. Assuming that the infrared limit of the
c-function is determined by the dimension of the associated Goldstone manifold,
we find that this c-function always decreases between the ultraviolet and
infrared fixed points.Comment: 8 pages, no figures, a few references adde
Collective Fields for QCD
A gauge-symmetric approach to effective Lagrangians is described with special
emphasis on derivations of effective low-energy Lagrangians from QCD. The
examples we discuss are based on exact rewritings of cut-off QCD in terms of
new collective degrees of freedom. These cut-off Lagrangians are thus
``effective'' in the sense that they explicitly contain some of the physical
long-distance degrees of freedom from the outset.(Talk presented by P.H.
Damgaard at the workshop on ``Quantum Field Theoretical Methods in High Energy
Physics'', Kyffhauser, Germany, Sept. 1993. To appear in those proceedings).Comment: LaTeX, 12 pages, CERN--TH-7035/9
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