Abstract

I will show how staggered or Kaehler-Dirac fermions suffer from a gravitational anomaly that can be computed exactly on a finite lattice. The anomaly breaks an exact onsite $U(1)$ symmetry to $Z_4$. This contradicts the usual folklore that anomalies can only arise in systems with an infinite number of degrees of freedom. It also evades the Nielsen-Ninomiya theorem since the $U(1)$ symmetry in question is not generated by $\gamma_5$. Furthermore, a mod 2 ‘t Hooft anomaly arises if we attempt to gauge this residual $Z_4$ symmetry which can only be cancelled if the system contains even numbers of flavors of staggered field. While the theory is not invariant under the usual chiral symmetry at non-zero lattice spacing, the naive continuum limit of the minimal anomaly free model in four dimensions nevertheless possesses the symmetries and matter representations of the Pati-Salam GUT - a chiral gauge theory containing the Standard Model. These conclusions are based on path integral methods but a Hamiltonian analysis is also possible and I will comment also on that.