Theories with global gauge anomalies on the lattice

TL;DR

This paper discusses the differences in how global gauge anomalies manifest in chiral gauge theories on the continuum versus on the lattice, highlighting the challenges in defining fermion measures on the lattice.

Contribution

It clarifies the relationship between continuum and lattice formulations of chiral gauge theories with global anomalies, emphasizing the reduced functional integral approach.

Findings

Continuum anomalies lead to zero fermion determinants over gauge fields.

Lattice formulations cannot define a fermion measure over all gauge configurations.

A reduced functional integral suffices for the existence of the theory on the lattice.

Abstract

A global anomaly in a chiral gauge theory manifests itself in different ways in the continuum and on the lattice. In the continuum case, functional integration of the fermion determinant over the whole space of gauge fields yields zero. In the case of the lattice, it is not even possible to define a fermion measure over the whole space of gauge configurations. However, this is not necessary, and as in the continuum, a reduced functional integral is sufficient for the existence of the theory.