Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

TL;DR

This paper introduces a versatile random matrix model that interpolates between different ensembles while preserving chiral symmetry, providing exact results for QCD-related spectral properties and validating them with simulations.

Contribution

It develops a new two-matrix random matrix model that captures symmetry transitions in QCD and derives exact spectral results in the microscopic limit.

Findings

Exact partition function and level density in the ε-regime of QCD

Model describes flavor symmetry breaking in various QCD contexts

Analytical results agree with Monte Carlo simulations

Abstract

We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3d QCD as well as in 4d QCD at high temperature or in 3d QCD at finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the $\varepsilon$-regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.