Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature

TL;DR

This paper derives universal microscopic spectral correlations of the unquenched QCD Dirac operator at finite temperature using random matrix theory, extending previous results to include temperature effects and non-zero topology.

Contribution

It introduces a new determinantal kernel for the microscopic eigenvalue correlations of the QCD Dirac operator at finite temperature, unifying and extending prior results.

Findings

Eigenvalue correlation functions expressed as determinants of temperature-dependent kernels

Universality of spectral correlations below the chiral phase transition

Extension to non-zero topological sectors

Abstract

In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting kernel and correlation functions in this class, which is the class of polynomial ensembles. We prove the equivalence between this new determinantal representation of the microscopic eigenvalue correlation functions and existing results in terms of determinants of different sizes, for an arbitrary number of quark flavours, with and without temperature, and extend them to non-zero topology. These results all agree and are thus universal when measured in units of the temperature dependent chiral condensate, as long as we stay below the chiral phase transition.