Study of some local and global $U(1)$ axial condensates in QCD at finite temperature

TL;DR

This paper investigates the behavior of local and global $U(1)$ axial condensates in high-temperature QCD, using spectral density analysis and instanton approximations, revealing their non-zero values and temperature dependence.

Contribution

It introduces nonperturbative analytical methods to study $U(1)$ axial condensates in the chirally restored phase of QCD, providing new insights into their temperature behavior.

Findings

$U(1)$ axial condensates remain non-zero at high temperatures

Derived asymptotic temperature dependence of condensates

Compared condensate behavior with topological susceptibility

Abstract

The aim of this work is to study some possible local and global $U(1)$ axial condensates in the high-temperature chirally restored phase of QCD, by means of two nonperturbative analytical techniques: (i) by expressing the functional averages in terms of the spectral density of the Euclidean Dirac operator and (ii) by evaluating the functional integrals in the instanton-background approximation. In this way, besides proving that these condensates are indeed different from zero in the high-temperature regime, we shall also derive their asymptotic temperature dependence and compare it with that of the topological susceptibility.