Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover

TL;DR

This paper analytically evaluates a unitary matrix integral relevant to low-energy QCD-like theories with real and pseudoreal quarks, and discusses its application to the GOE-GUE crossover in random matrix theory.

Contribution

It provides explicit pfaffian expressions for these integrals, advancing analytical tools for studying QCD-like theories at finite chemical potential.

Findings

Derived pfaffian expressions for the matrix integrals.

Applied results to analyze the GOE-GUE crossover.

Extended methods to theories with pseudoreal quarks.

Abstract

A unitary matrix integral that appears in the low-energy limit of QCD-like theories with quarks in real representations of the gauge group at finite chemical potential is analytically evaluated and expressed as a pfaffian. Its application to the GOE-GUE crossover in random matrix theory is discussed. An analogous unitary integral for QCD-like theories with quarks in pseudoreal representations of the gauge group is also evaluated.