Lattice chiral gauge theories through gauge fixing

TL;DR

This paper reviews the challenges in formulating lattice chiral gauge theories and presents evidence that abelian theories can be constructed non-perturbatively via gauge fixing, with insights into fermion-number violation.

Contribution

It demonstrates that abelian lattice chiral gauge theories can be non-perturbatively built using gauge fixing, advancing the understanding of lattice gauge theory construction.

Findings

Abelian lattice chiral gauge theories can be constructed non-perturbatively.

Evidence supports the gauge-fixing approach for abelian theories.

Fermion-number violating processes are realized in this framework.

Abstract

After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we discuss the analytic and numerical evidence that abelian lattice chiral gauge theories can be non-perturbatively constructed through the gauge-fixing approach. While a complete non-abelian extension is still under construction, we also show how fermion-number violating processes are realized in this approach.