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

## TL;DR

This paper investigates the one-loop effective action in a lattice chiral gauge theory, revealing local interactions between the gauge field and its gradient flow counterpart, which may lead to gauge symmetry-breaking effects.

## Contribution

It demonstrates that the continuum limit of the one-loop effective action includes non-vanishing local interactions between A and A_star, indicating potential gauge symmetry issues.

## Key findings

- Local interaction terms between A and A_star are present at one-loop.
- These interactions do not vanish even in anomaly-free representations.
- Such interactions can cause gauge symmetry-breaking effects.

## Abstract

We study the one-loop effective action defined by the chiral overlap operator in the four-dimensional lattice formulation of chiral gauge theories by Grabowska and Kaplan. In the tree-level continuum limit, the left-handed component of the fermion is coupled only to the original gauge field~$A$, while the right-handed one is coupled only to~$A_\star$, which is given by the gradient flow of~$A$ with infinite flow time. In this paper, we show that the continuum limit of the one-loop effective action contains local interaction terms between $A$ and~$A_\star$, which do not generally vanish even if the gauge representation of the fermion is anomaly free. We argue that the presence of such interaction terms can be regarded as undesired gauge symmetry-breaking effects in the formulation.