Eigenvalue Distributions of the QCD Dirac Operator

We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge theory with staggered fermions. Very precise agreement is found in all cases. As a simple by-product we also extract the microscopic spectral density of the Dirac operator in SU(3) gauge theory with dynamical massive fermions for $N_f=1$ and 2, and obtain high-accuracy agreement with analytical expressions.Comment: LaTeX, 8 pages, 9 postscript figures. Very minor correction

Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor

We consider the effect of a non-zero lattice spacing on the low-energy effective theory of Wilson fermions with one flavor. Analytical results are given for both the chiral condensate and the microscopic spectral density of the Wilson Dirac operator. A subtle mechanism ensures that a constant chiral condensate is recovered, once the sum over sectors of fixed index is performed.Comment: 6 pages, 8 figure

Finite-volume meson propagators in quenched chiral perturbation theory

We compute meson propagators in finite-volume quenched chiral perturbation theory.Comment: 3 pages, Lattice2001(chiral fermions

The QCD Dirac Operator Spectrum and Finite-Volume Scaling

Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.Comment: LATTICE98(confine

Partially quenched chiral perturbation theory in the epsilon-regime

We calculate meson correlators in the epsilon-regime within partially quenched chiral perturbation theory. The valence quark masses and sea quark masses can be chosen arbitrary and all non-degenerate. Taking some of the sea quark masses to infinity, one obtains a smooth connection among the theories with different number of flavors, as well as the quenched theory. These results can be directly compared with lattice QCD simulations.Comment: 40pages, 7figures, Minor changes, references adde

Smooth Non-Abelian Bosonization

We present an extension of ``smooth bosonization'' to the non-Abelian case. We construct an enlarged theory containing both bosonic and fermionic fields which exhibits a local chiral gauge symmetry. A gauge fixing function depending on one real parameter allows us to interpolate smoothly between a purely fermionic and a purely bosonic representation. The procedure is, in the special case of bosonization, complementary to the approach based on duality.Comment: LaTeX, 13 pages, CERN--TH-7347/9

Partially Quenched Chiral Condensates from the Replica Method

A large-N_f expansion is used to compute the partially quenched chiral condensate of QCD in the microscopic finite-volume scaling region.Comment: LaTeX, 7 page

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

Determining F_pi from spectral sum rules

We derive spectral sum rules for a system with two quarks coupled to an imaginary isospin chemical potential in the \epsilon regime. The sum rules show an explicit dependence on the pion decay constant which should make it possible to measure F_pi from the eigenvalue spectrum of this particular Dirac operator.Comment: 8 page