Global Anomalies in chiral gauge theories on the lattice

TL;DR

This paper investigates global anomalies in chiral gauge theories on the lattice, demonstrating that certain SU(2) theories exhibit anomalies analogous to Witten's continuum results, affecting the consistency of fermionic measures.

Contribution

It establishes the presence of SU(2) global anomalies on the lattice for fundamental Weyl fermions, linking lattice obstructions to known continuum anomalies.

Findings

SU(2) theory with fundamental Weyl fermion has a global anomaly

Obstructions prevent consistent fermionic measure on the lattice

Lattice anomaly corresponds to Witten's SU(2) anomaly in continuum

Abstract

We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Luscher's approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU(2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show that this obstruction is the lattice analogue of the SU(2) anomaly first discovered by Witten.