Sneaking up on lattice chiral fermions

Professor Simon Catterall

I will show how staggered 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 the usual chiral symmetry. Furthermore, a mod 2 't Hooft anomaly arises if we attempt to gauge this residual $Z_4$ symmetry which can only be canceled if the system contains even numbers of flavors of staggered field. Remarkably, 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.