Parity Invariant Lattice Regularization of Three-Dimensional Gauge-Fermion System

TL;DR

This paper develops a lattice regularization for three-dimensional massless Dirac fermions that preserves parity invariance, enabling non-perturbative studies without fine-tuning.

Contribution

It introduces a parity-invariant lattice formulation using the overlap formalism, contrasting with Wilson fermions, for three-dimensional gauge-fermion systems.

Findings

Parity-invariant regularization achieved with overlap formalism

Contrasts with Wilson fermion approach in the massless limit

Facilitates non-perturbative studies of gauge-fermion interactions

Abstract

In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. We construct a lattice formulation of the massless Dirac fermion using the overlap formalism. We show that the result is parity invariant in contrast to the formulation using Wilson fermions in the massless limit. This facilitates a non-perturbative study of three-dimensional massless Dirac fermions interacting with a gauge field in a parity invariant setting with no need for fine-tuning.