1,687 research outputs found
The Replica Method and Toda Lattice Equations for QCD_3
We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the
leading term of the effective partition function satisfies a set of Toda
lattice equations, recursive in the number of flavors. Taking the replica limit
of these Toda equations allows us to derive the microscopic spectral
correlation functions for the QCD Dirac operator in 3 dimensions. For an even
number of flavors we reproduce known results derived using other techniques. In
the case of an odd number of flavors the theory has a severe sign problem, and
we obtain previously unknown microscopic spectral correlation functions.Comment: 18 pages, 2 figure
Topology and the Dirac Operator Spectrum in Finite-Volume Gauge Theories
The interplay between between gauge-field winding numbers, theta-vacua, and
the Dirac operator spectrum in finite-volume gauge theories is reconsidered. To
assess the weight of each topological sector, we compare the mass-dependent
chiral condensate in gauge field sectors of fixed topological index with the
answer obtained by summing over the topological charge. Also the microscopic
Dirac operator spectrum in the full finite-volume Yang-Mills theory is obtained
in this way, by summing over all topological sectors with the appropriate
weight.Comment: LaTeX, 21 pages. One reference adde
Meson Correlation Functions in the epsilon-Regime
We present a numerical pilot study of the meson correlation functions in the
epsilon-regime of chiral perturbation theory. Based on simulations with overlap
fermions we measured the axial and pseudo-scalar correlation functions, and we
discuss the implications for the leading low energy constants in the chiral
Lagrangian.Comment: 3 pages, 3 figures, talk presented at Lattice2003(chiral
Simulating chiral quarks in the epsilon-regime of QCD
We present simulation results for lattice QCD with chiral fermions in small
volumes, where the epsilon-expansion of chiral perturbation theory applies. Our
data for the low lying Dirac eigenvalues, as well as mesonic correlation
functions, are in agreement with analytical predictions. This allows us to
extract values for the leading Low Energy Constants F_{pi} and Sigma.Comment: 4 pages, talk presented by W.B. at Baryons04 (Paris, October 25 - 29,
2004); one Ref. adde
Chiral symmetry breaking at large N_c
We present numerical evidence for the hypothesis that, in the planar limit,
four dimensional Euclidean Yang-Mills theory on a finite symmetrical four-torus
breaks chiral symmetry spontaneously when the length of the sides l is larger
than a critical value l_c with a bilinear condensate whose value is independent
of l. Therefore spontaneous symmetry breaking occurs at finite volume and
infinite N_c reduction holds for the chiral condensate.Comment: 43 pages, 16 figures, 1 table, more typos correcte
Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
We introduce a random two-matrix model interpolating between a chiral
Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without
symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE)
and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n
limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit)
this theory is in one to one correspondence to the partition function of Wilson
chiral perturbation theory in the epsilon regime, such as the related two
matrix-model previously introduced in refs. [20,21]. For a generic number of
flavours and rectangular block matrices in the chGUE part we derive an
eigenvalue representation for the partition function displaying a Pfaffian
structure. In the quenched case with nu=0,1 we derive all spectral correlations
functions in our model for finite-n, given in terms of skew-orthogonal
polynomials. The latter are expressed as Gaussian integrals over standard
Laguerre polynomials. In the weakly non-chiral microscopic limit this yields
all corresponding quenched eigenvalue correlation functions of the Hermitian
Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio
Exact Vacuum Energy of Orbifold Lattice Theories
We investigate the orbifold lattice theories constructed from supersymmetric
Yang-Mills matrix theories (mother theories) with four and eight supercharges.
We show that the vacuum energy of these theories does not receive any quantum
correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references
corrected, comments adde
Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
We derive the hole probability and the distribution of the smallest
eigenvalue of chiral hermitian random matrices corresponding to Dirac operators
coupled to massive quarks in QCD. They are expressed in terms of the QCD
partition function in the mesoscopic regime. Their universality is explicitly
related to that of the microscopic massive Bessel kernel.Comment: 4 pages, 1 figure, REVTeX. Minor typos in subscripts corrected.
Version to appear in Phys. Rev.
Universal and non-universal behavior in Dirac spectra
We have computed ensembles of complete spectra of the staggered Dirac
operator using four-dimensional SU(2) gauge fields, both in the quenched
approximation and with dynamical fermions. To identify universal features in
the Dirac spectrum, we compare the lattice data with predictions from chiral
random matrix theory for the distribution of the low-lying eigenvalues. Good
agreement is found up to some limiting energy, the so-called Thouless energy,
above which random matrix theory no longer applies. We determine the dependence
of the Thouless energy on the simulation parameters using the scalar
susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure
Mesoscopic QCD and the Theta Vacua
The partition function of QCD is analyzed for an arbitrary number of flavors,
N_f, and arbitrary quark masses including the contributions from all
topological sectors in the Leutwyler--Smilga regime. For given N_f and
arbitrary vacuum angle, \theta, the partition function can be reduced to N_f-2
angular integrations of single Bessel functions. For two and three flavors, the
\theta dependence of the QCD vacuum is studied in detail. For N_f= 2 and 3, the
chiral condensate decreases monotonically as \theta increases from zero to \pi
and the chiral condensate develops a cusp at \theta=\pi for degenerate quark
masses in the macroscopic limit. We find a discontinuity at \theta=\pi in the
first derivative of the energy density with respect to \theta for degenerate
quark masses. This corresponds to the first--order phase transition in which CP
is spontaneously broken, known as Dashen's phenomena.Comment: 31 pages, revtex, 10 figures, final version to appear in Nucl. Phys.
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