A calculation of the gauge anomaly with the chiral overlap operator

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.

14 pages

References in corpus (9)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Nonperturbative Regulator for Chiral Gauge Theories?
• A Chiral Solution to the Ginsparg-Wilson Equation
• Axial U(1) current in Grabowska and Kaplan's formulation
• Six-dimensional regularization of chiral gauge theories
• Fermion number anomaly with the fluffy mirror fermion
• Lorentz symmetry violation in the fermion number anomaly with the chiral overlap operator
• One-loop perturbative coupling of $A$ and $A_{\star }$ through the chiral overlap operator