Six-dimensional regularization of chiral gauge theories

TL;DR

This paper introduces a novel six-dimensional regularization method for four-dimensional chiral gauge theories using domain-wall fermions, enabling non-perturbative lattice regularization and anomaly cancellation.

Contribution

It proposes a six-dimensional Dirac fermion framework with domain-walls that naturally encode gauge and global anomalies, facilitating non-perturbative lattice regularization of chiral gauge theories.

Findings

The formulation reproduces the anomaly descent equations from six to four dimensions.

It ensures anomaly cancellation through the interplay of axial U(1) and parity anomalies.

The approach allows for a non-perturbative lattice regularization using the fermion determinant.

Abstract

We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain-walls. One domain-wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six-dimensions to the gauge anomaly in four-dimensions. Another domain-wall implies a similar inflow of the global anomalies. The anomaly free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is based on a massive vector-like fermion determinant, a non-perturbative regularization will be possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.