Complex spacing ratios of the non-Hermitian Dirac operator in universality classes AI$^\dagger$ and AII$^\dagger$

TL;DR

This paper investigates the spectral properties of non-Hermitian Dirac operators in QCD-like theories, demonstrating their classification into specific universality classes and confirming predictions through eigenvalue spacing ratio analysis.

Contribution

It establishes the universality class of non-Hermitian Dirac operators in different fermion representations and verifies these classifications via lattice computations.

Findings

Dirac operators in certain theories belong to universality classes AI$^$ or AII$^$

Eigenvalue spacing ratios follow universal distributions without unfolding

Reversal of correspondence for staggered fermions on the lattice

Abstract

We consider non-Hermitian Dirac operators in QCD-like theories coupled to a chiral U(1) potential or an imaginary chiral chemical potential. We show that in the continuum they fall into the recently discovered universality classes AI$^\dagger$ or AII$^\dagger$ of random matrix theory if the fermions transform in pseudoreal or real representations of the gauge group, respectively. For staggered fermions on the lattice this correspondence is reversed. We verify our predictions by computing spacing ratios of complex eigenvalues, whose distribution is universal without the need for unfolding.