Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions

TL;DR

This paper derives finite-volume QCD partition functions using chiral random matrix ensembles at beta=1 and 4, connecting random matrix theory with QCD in the ergodic regime, and provides explicit formulas for eigenvalue correlations.

Contribution

It introduces new expressions for QCD partition functions in terms of microscopically rescaled masses using chiral orthogonal and symplectic ensembles, extending previous results.

Findings

Derived explicit formulas for QCD partition functions

Connected random matrix ensembles with QCD in the ergodic regime

Reproduced known sigma model results for degenerate masses

Abstract

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition functions are derived in terms of microscopically rescaled mass variables. In limited cases, correlation functions of Dirac eigenvalues and distributions of the smallest Dirac eigenvalue are given as ratios of these partition functions. When all masses are degenerate, our results reproduce the known expressions for the partition functions of zero-dimensional sigma models.