Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD

TL;DR

This paper introduces an instanton-based random matrix model to understand chiral symmetry behavior in high-temperature QCD, revealing a persistent spectral singularity and implications for U(1)_A symmetry breaking.

Contribution

It presents a novel instanton-based random matrix model that captures the spectral properties of QCD at high temperatures, highlighting the role of instantons in chiral symmetry realization.

Findings

Spectral density exhibits a singularity at the origin due to a dilute instanton gas.

Small instanton-antiinstanton molecules do not affect the spectral singularity.

Chiral condensate vanishes for two massless flavors in the chiral limit.

Abstract

We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures.