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

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.