New universality classes of the non-Hermitian Dirac operator in QCD-like theories

TL;DR

This paper identifies new universality classes for the non-Hermitian Dirac operator in QCD-like theories, connecting lattice simulations, random matrix theory, and spectral sum rules to advance understanding of spectral correlations.

Contribution

It introduces new universality classes for the non-Hermitian Dirac operator in two-color QCD with specific gauge fields and representations, supported by lattice simulations and theoretical predictions.

Findings

Identification of universality classes AI† and AII† for the Dirac operator

Verification of predictions through lattice simulations with staggered fermions

Derivation of novel spectral sum rules

Abstract

In non-Hermitian random matrix theory there are three universality classes for local spectral correlations: the Ginibre class and the nonstandard classes $\mathrm{AI}^\dagger$ and $\mathrm{AII}^\dagger$. We show that the continuum Dirac operator in two-color QCD coupled to a chiral $\mathrm{U}(1)$ gauge field or an imaginary chiral chemical potential falls in class $\mathrm{AI}^\dagger$ ($\mathrm{AII}^\dagger$) for fermions in pseudoreal (real) representations of $\mathrm{SU}(2)$. We introduce the corresponding chiral random matrix theories and verify our predictions in lattice simulations with staggered fermions, for which the correspondence between representation and universality class is reversed. Specifically, we compute the complex eigenvalue spacing ratios introduced recently. We also derive novel spectral sum rules.