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We consider non-Hermitian Dirac operators in QCD-like theories coupled to achiral U(1) potential or an imaginary chiral chemical potential. We show thatin the continuum they fall into the recently discovered universality classesAI$^\dagger$ or AII$^\dagger$ of random matrix theory if the fermions transformin pseudoreal or real representations of the gauge group, respectively. Forstaggered fermions on the lattice this correspondence is reversed. We verifyour predictions by computing spacing ratios of complex eigenvalues, whosedistribution is universal without the need for unfolding.

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