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

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