Topology and chiral random matrix theory at nonzero imaginary chemical potential

TL;DR

This paper investigates how topology influences the spectral properties of a random matrix model of QCD at nonzero imaginary chemical potential or temperature, revealing the necessity of normalization factors for correct $ heta$-dependence.

Contribution

It demonstrates that the topological domain of the Dirac spectrum extends beyond the microscopic domain at nonzero imaginary chemical potential or temperature, affecting the $ heta$-dependence.

Findings

Normalization factors cancel to reproduce QCD $ heta$-dependence

Topological domain extends beyond microscopic domain at nonzero imaginary chemical potential

Behavior may persist in certain lattice QCD formulations

Abstract

We study the effect of topology for a random matrix model of QCD at nonzero imaginary chemical potential or nonzero temperature. Non-universal fluctuations of Dirac eigenvalues lead to normalization factors that contribute to the $\theta$-dependence of the partition function. These normalization factors have to be canceled in order to reproduce the $\theta$-dependence of the QCD partition function. The reason for this behavior is that the topological domain of the Dirac spectrum (the region of the Dirac spectrum that is sensitive to the topological charge) extends beyond the microscopic domain at nonzero imaginary chemical potential or temperature. Such behavior could persist in certain lattice formulations of QCD.