Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions

We study 't Hooft anomaly matching in lattice models with strong Yukawa or multi-fermion interactions. Strong non-gauge interactions among the mirror fermions in a vectorlike lattice gauge theory are introduced with the aim to obtain, in a strong-coupling symmetric phase, a long-distance unbroken gauge theory with chiral fermions in a complex representation. We show how to use exact lattice chirality to analyze the anomaly matching conditions on chiral symmetry current correlators at finite lattice spacing and volume. We perform a Monte Carlo study of the realization of anomaly matching in a toy two-dimensional model with an anomalous mirror-fermion content at strong mirror Yukawa coupling. We show that 't Hooft anomaly matching is satisfied, in most of the phase diagram, via the minimal solution in either the massless fermion or "Goldstone" mode, while in some cases there are extra massless vectorlike mirror fermions. The mirror spectrum at strong coupling is thus consistent with long-distance unitarity. We discuss the implications of our results for future studies of the most interesting case of the decoupling of anomaly-free mirror-fermion sectors.