The zeros of the QCD partition function

TL;DR

This paper links the zeros of the QCD partition function to Dirac operator spectra, using chiral Random Matrix Theory, revealing universal features and the impact of finite Thouless energy.

Contribution

It introduces a formal connection between partition function zeros and spectral properties in QCD, incorporating the concept of normal modes and universality considerations.

Findings

Zeros of the QCD partition function relate to Dirac spectra.

Finite Thouless energy influences the partition function zeros.

Certain features of the partition function are universal.

Abstract

We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and applies to QCD when chiral symmetry is spontaneously broken. Further, we introduce and examine the concept of normal modes in chiral spectra. Using this formalism we study the consequences of a finite Thouless energy for the zeros of the partition function. This leads to the demonstration that certain features of the QCD partition function are universal.