Topology and the Dirac Spectrum in Hot QCD

TL;DR

This paper investigates the unexpected behavior of the Dirac spectral density in hot QCD, revealing that topological effects and instanton-antiinstanton mixing influence chiral symmetry restoration above the critical temperature.

Contribution

It demonstrates that the nonvanishing topological susceptibility leads to a finite eigenvalue density near zero, challenging previous assumptions about chiral symmetry restoration in hot QCD.

Findings

Spectral density develops a zero-mode peak above critical temperature

Eigenmode statistics suggest instanton-antiinstanton mixing

Topological susceptibility correlates with eigenvalue density near zero

Abstract

It is known that contrary to expectations, the order parameter of chiral symmetry breaking, the Dirac spectral density at zero virtuality does not vanish above the critical temperature of QCD. Instead, the spectral density develops a pronounced peak at zero. We show that the spectral density in the peak has large violations of the expected volume scaling. This anomalous scaling and the statistics of these eigenmodes is consistent with them being produced by mixing instanton and antiinstanton zero modes. Consequently, we show that a nonvanishing topological usceptibility implies a finite density of eigenvalues around zero, which can have implications on the restoration of chiral symmetry above the critical temperature.