Staggered fermions for chiral gauge theories: Test on a two-dimensional axial-vector model

TL;DR

This paper explores the use of staggered fermions in two-dimensional chiral gauge theories, demonstrating that gauge invariance is restored in the continuum limit and analyzing current divergence relations both analytically and numerically.

Contribution

It provides a first step towards lattice chiral models with staggered fermions by studying a 2D axial-vector U(1) model and analyzing current divergences.

Findings

Continuum divergence relations are reproduced up to contact terms.

Gauge invariance is restored in the classical continuum limit.

Numerical studies confirm the analytical divergence relations for smooth gauge fields.

Abstract

As a first step towards constructing chiral models on the lattice with staggered fermions, we study a U(1) model with axial-vector coupling to an external gauge field in two dimensions. In our approach gauge invariance is broken, but it is restored in the classical continuum limit. We find that the continuum divergence relations for the vector and axial-vector currents are reproduced, up to contact terms, which we determine analytically. The current divergence relations are also studied numerically for smooth external gauge fields with topological charge zero. We furthermore investigate the effect of fluctuating gauge transformations and of gauge configurations with non-trivial topological charge.