Global obstructions to gauge-invariance in chiral gauge theory on the lattice

TL;DR

This paper demonstrates that global obstructions to gauge invariance in chiral gauge theories, identified in the continuum, are accurately reproduced on the lattice using the Overlap formulation, linking continuum anomaly conditions to lattice formulations.

Contribution

It establishes a precise correspondence between continuum gauge anomalies and lattice obstructions in the Overlap formulation, highlighting the necessity of anomaly cancellation conditions on the lattice.

Findings

Global obstructions are reproduced on the lattice at small lattice spacing.

Continuum anomaly cancellation condition is necessary for lattice anomaly cancellation.

Overlap formulation accurately captures continuum gauge anomalies.

Abstract

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition $d_R^{abc}=0$ is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation.