A calculation of the gauge anomaly with the chiral overlap operator

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. 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 are equivalent to those known in the continuum theory up to total derivatives.