Six-dimensional regularization of chiral gauge theories on a lattice

TL;DR

This paper introduces a novel six-dimensional regularization method for four-dimensional chiral gauge theories using domain-wall fermions, embedding anomaly cancellation conditions and extending gauge fields via gradient flow.

Contribution

It presents a new six-dimensional framework with domain-wall profiles to regularize chiral gauge theories, naturally incorporating anomaly descent and inflow mechanisms.

Findings

Successfully embeds anomaly cancellation conditions in six dimensions.

Demonstrates the natural emergence of Weyl fermions at domain-wall junctions.

Extends gauge fields into the bulk using gradient flow for consistent four-dimensional path integrals.

Abstract

We propose a six-dimensional regularization of four dimensional chiral gauge theories. We consider a massive Dirac fermion in six dimensions with two different operators having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of the two domain-walls. In our formulation, 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, is naturally embedded. Moreover, a similar inflow of the global anomalies is found. 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. 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.