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We show how a path integral for reduced K\"{a}hler-Dirac fermions suffersfrom a phase ambiguity associated with the fermion measure that is an analog ofthe measure problem seen for chiral fermions. However, unlike the case ofchiral symmetry, a doubler free lattice action exists which is invariant underthe corresponding onsite symmetry. This allows for a clear diagnosis andsolution to the problem using mirror fermions resulting in a unique gaugeinvariant measure. By introducing an appropriate set of Yukawa interactionswhich are consistent with 't Hooft anomaly cancellation we conjecture themirrors can be decoupled from low energy physics. Moreover, the minimal suchK\"{a}hler-Dirac mirror model yields a light sector which corresponds, in theflat space continuum limit, to the Pati-Salam GUT model.

Lattice Regularization of Reduced K\"{a}hler-Dirac Fermions and Connections to Chiral Fermions