Exact lattice anomalies and a possible path to lattice chiral gauge theories

I will discuss a new class of gravitational anomaly that arises for Kaehler-Dirac fermions. I will start by showing how the latter are related to Dirac fermions in flat space and then show how such theories may be discretized on a curved space. I will then show how such theories possess anomalies that survive discretization in contradiction to the usual folklore that anomalies can only be realized in theories with infinite numbers of degrees of freedom. The presence of exact 't Hooft anomalies strongly constrains the I.R phases of such theories. Specifically, cancellation of all 't Hooft anomalies is a necessary condition for symmetric mass generation -- the mechanism by which fermions can be given mass without breaking any symmetries. Using this result one can build mirror models of Kaehler-Dirac fields whose low energy spectra target particular chiral gauge theories -- the simplest being the Pati-Salam GUT model.