Massive chiral random matrix ensembles at beta = 1 & 4 : QCD Dirac operator spectra

TL;DR

This paper explores the spectra of Dirac operators in QCD-like theories using chiral random matrix ensembles at beta=1 and 4, deriving correlation functions that interpolate between different physical limits.

Contribution

It introduces new Pfaffian-based correlation functions for Dirac eigenvalues in QCD with finite quark masses, expanding the understanding of spectral properties in these theories.

Findings

Derived correlation functions expressed as Pfaffians.

Interpolated between chiral and quenched limits.

Applicable to sectors with arbitrary topological charge.

Abstract

The zero momentum sectors in effective theories of QCD coupled to pseudoreal (two colors) and real (adjoint) quarks have alternative descriptions in terms of chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, we compute correlation functions of Dirac operator eigenvalues within a sector with an arbitrary topological charge in a presence of finite quark masses of the order of the smallest Dirac eigenvalue. These novel correlation functions, expressed in terms of Pfaffians, interpolate between known results for the chiral and quenched limits as quark masses vary.