# A Lattice Formulation of Chiral Gauge Theories

## TL;DR

This paper introduces a lattice formulation for chiral gauge theories that employs a Wilson mass and a double limit process to maintain gauge invariance, applicable to anomaly-free fermion representations.

## Contribution

It proposes a novel lattice approach for chiral gauge theories using a Wilson mass and a double limit to restore gauge invariance, addressing longstanding issues in lattice chiral fermion formulations.

## Key findings

- Method effectively removes fermion doublers.
- Restores gauge invariance in anomaly-free theories.
- Provides a technique for computing fermion operator matrix elements.

## Abstract

We present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken, in which the lattice spacing associated with the fermion field is sent to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. We also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that the computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.