$U(1)_A$ Breaking in Hot QCD in the Chiral Limit

TL;DR

This paper introduces an instanton-based random matrix model for hot QCD that accurately reproduces lattice eigenvalue distributions and predicts $U(1)_A$ symmetry breaking effects in the thermodynamic limit.

Contribution

It presents a novel instanton-inspired random matrix model that captures spectral properties of hot QCD and offers predictions for chiral symmetry breaking phenomena.

Findings

Spectral density peaks become singular at zero in the thermodynamic limit.

The model reproduces lattice eigenvalue distributions in the quenched case.

Predictions for physical quantities related to chiral symmetry breaking.

Abstract

We propose a simple instanton-based random matrix model of hot QCD that in the quenched case precisely reproduces the distribution of the lowest lattice overlap Dirac eigenvalues. Even after including dynamical quarks the model can be easily simulated in volumes and for quark masses that will be out of reach for direct lattice simulations in the foreseeable future. Our simulations show that quantities connected to the $U(1)_A$ and $SU(N_f)_A$ chiral symmetry are dominated by eigenvalues in a peak of the spectral density that becomes singular at zero in the thermodynamic limit. This spectral peak turns out to be produced by an ideal instanton gas. By generalizing Banks-Casher type integrals for the singular spectral density, definite predictions can be given for physical quantities that are essential to test chiral symmetry breaking, but presently impossible to compute reliably with direct lattice simulations.