Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion

TL;DR

This paper investigates parity anomaly cancellation in a three-dimensional QED with a single massless fermion, demonstrating non-perturbative cancellation on the lattice and spontaneous parity breaking in the infinite volume limit.

Contribution

It provides the first non-perturbative lattice evidence that parity anomaly cancels exactly in the continuum limit for this model.

Findings

Parity-breaking terms vanish in the continuum limit at finite volume.

Parity invariance is spontaneously broken in the infinite volume limit.

Numerical evidence supports the theoretical expectation of anomaly cancellation.

Abstract

We study a three-dimensional non-compact QED with a single two-component massless fermion and two infinitely massive regulator fermions of half the charge using lattice overlap formalism. The parity anomaly is expected to cancel exactly between the massless and regulator fermions in the continuum, but this cancellation is inexact on lattice akin to lattice chiral gauge theories. We show non-perturbatively that parity-breaking terms vanish in the continuum limit at any finite volume. We present numerical evidences that the resulting parity-invariant theory spontaneously breaks parity in the infinite volume limit.