Massive random matrix ensembles at beta = 1 & 4 : QCD in three dimensions

TL;DR

This paper explores the connection between three-dimensional QCD with specific quark types and random matrix ensembles, deriving finite-volume partition functions and eigenvalue correlations using quaternion determinants.

Contribution

It establishes a novel correspondence between QCD in three dimensions and orthogonal and symplectic random matrix ensembles, providing explicit finite-volume correlation functions.

Findings

Derived finite-volume QCD partition functions.

Computed eigenvalue correlation functions using quaternion determinants.

Reduced correlation functions to Gaussian ensemble results in the quenched limit.

Abstract

The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and symplectic ensembles of random matrices. Using this correspondence, we compute finite-volume QCD partition functions and correlation functions of Dirac operator eigenvalues in a presence of finite quark masses of the order of the smallest Dirac eigenvalue. These novel correlation functions, expressed in terms of quaternion determinants, are reduced to conventional results for the Gaussian ensembles in the quenched limit.