Chiral invariance and lattice fermions with minimal doubling

TL;DR

This paper investigates a lattice fermion action with a Wilson-like term that preserves chiral invariance but breaks hypercubic symmetry, demonstrating conditions under which the theory is reflection positive and physically consistent.

Contribution

It shows that for certain parameter ranges, the lattice fermion action maintains reflection positivity and has physically meaningful propagator poles, advancing lattice fermion formulations.

Findings

The action describes two Dirac fields in the continuum limit.

The theory is link-reflection positive for 1/2 < λ ≤ 1.

The propagator has real energy poles as expected.

Abstract

A few years ago some attention has been given to a fermionic action on the lattice, with a Wilson-like term which is chirally invariant but breaks the hypercubic space-time lattice symmetry. This action describes two Dirac fields in the continuum limit, provided the coefficient $\lambda$ of the Wilson-like term satisfies $\lambda > \frac{1}{2}$. In this letter it is shown that for $\frac{1}{2} < \lambda \leq 1$ the theory is link-reflection positive. The propagator has the expected real energy poles. Modulo a phase shift on the fermions, the only relevant terms which can be added to the action respecting its symmetries have dimension $4$.