Vacuum alignment and lattice artifacts

TL;DR

This paper explores how vacuum alignment and lattice artifacts influence symmetry breaking in gauge theories, using chiral Lagrangian techniques to analyze examples like Wilson and staggered fermions.

Contribution

It provides a detailed analysis of the interplay between vacuum alignment and lattice artifacts, correcting recent misconceptions about staggered fermions.

Findings

Vacuum tends to align to keep gauged subgroup unbroken

Lattice discretization can induce new symmetry-breaking phases

Recent claims about staggered fermions are shown to be incorrect

Abstract

When a subgroup of the flavor symmetry group of a gauge theory is weakly coupled to additional gauge fields, the vacuum tends to align such that the gauged subgroup is unbroken. At the same time, the lattice discretization typically breaks the flavor symmetry explicitly, and can give rise to new lattice-artifact phases with spontaneously broken symmetries. We discuss the interplay of these two phenomena, using chiral lagrangian techniques. Our first example is two-flavor Wilson QCD coupled to electromagnetism. We also consider examples of theories with staggered fermions, and demonstrate that recent claims in the literature based on the use of staggered fermions are incorrect.