A calculation of the gauge anomaly with the chiral overlap operator

TL;DR

This paper derives a general expression for calculating gauge anomalies using the chiral overlap operator in various dimensions, confirming its consistency with known continuum anomalies in the continuum limit.

Contribution

It provides a new method to compute gauge anomalies with the chiral overlap operator, extending to arbitrary even dimensions and treating boundary gauge fields independently.

Findings

Gauge anomalies match known continuum results in 2, 4, and 6 dimensions.

Derived a general expression for anomalies with the chiral overlap operator.

Confirmed the operator's consistency with continuum gauge anomaly calculations.

Abstract

We investigate the property of the effective action with the chiral overlap operator, which was derived by Grabowska and Kaplan. They proposed a lattice formulation of four-dimensional chiral gauge theory, which is derived from their domain-wall formulation. In this formulation, an extra dimension is introduced and the gauge field along the extra dimension is evolved by the gradient flow. The chiral overlap operator satisfies the Ginsparg-Wilson relation and only depends on the gauge fields on the two boundaries. In this paper, we start from the arbitrary even-dimensional chiral overlap operator. We treat the gauge fields on the two boundaries independently, and derive the general expression to calculate the gauge anomaly with the chiral overlap operator in the continuum limit. As a result, we show that the gauge anomalies with the chiral overlap operator in two, four, and six dimensions in the continuum limit is equivalent to those known in the continuum theory up to total derivatives.