One-loop perturbative coupling of $A$ and $A_\star$ through the chiral overlap operator

TL;DR

This paper analyzes the one-loop effective action in a lattice formulation of chiral gauge theories, revealing local interactions between gauge fields that could affect the theory's spectrum.

Contribution

It demonstrates that the one-loop effective action contains local interactions between $A$ and $A_star$, which persist even with anomaly cancellation, indicating potential issues in the formulation.

Findings

Local interaction terms between $A$ and $A_star$ in the effective action.

Presence of these interactions at the one-loop level.

Implications for the perturbative spectrum of the theory.

Abstract

Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the original gauge field~$A$, while the right-handed one is coupled only to the gauge field~$A_\star$, a deformation of~$A$ by the gradient flow with infinite flow time. In this paper, we study the fermion one-loop effective action in their formulation. We show that the continuum limit of this effective action contains local interaction terms between $A$ and~$A_\star$, even if the anomaly cancellation condition is met. These non-vanishing terms would lead an undesired perturbative spectrum in the formulation.