Non-gauge fixing approach to chiral gauge theories using staggered fermions

TL;DR

This paper explores a gauge-invariance-restoring approach for chiral gauge theories on the lattice using staggered fermions, aiming to avoid gauge fixing by relying on dynamical restoration in a U(1) model.

Contribution

It proposes a non-gauge fixing method for constructing chiral gauge theories with staggered fermions, focusing on dynamical gauge invariance restoration.

Findings

Gauge symmetry breaking can be dynamically restored in the continuum limit.

The approach is demonstrated in a four-dimensional U(1) axial-vector model.

Potential for constructing gauge-invariant chiral theories without gauge fixing.

Abstract

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the non-gauge invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory. This scenario is very attractive since it does not rely on gauge fixing. We investigate a simple realization of this approach in a U(1) axial-vector model with dynamical fermions in four dimensions.