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

Understand

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.