't Hooft vertices, partial quenching, and rooted staggered QCD

TL;DR

This paper analyzes 't Hooft vertices in rooted staggered QCD, demonstrating that unphysical vertices do not hinder the continuum limit or the recovery of taste symmetry, thus supporting the validity of rooted staggered fermions.

Contribution

It clarifies the properties of 't Hooft vertices in partially quenched and rooted QCD, resolving paradoxes and countering claims that question the validity of rooted staggered fermions.

Findings

't Hooft vertices in the physical subspace have the expected form.

Unphysical 't Hooft vertices do not prevent taste symmetry restoration.

Rooted staggered QCD remains valid despite unphysical correlation functions.

Abstract

We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We resolve an apparent paradox that arises when one uses rooted staggered fermions to study one-flavor QCD, by showing how, in partially quenched theories, it is possible to have spontaneous symmetry breaking of a non-anomalous symmetry in finite volume. Using these results, we demonstrate that arguments recently given by Creutz--claiming to disprove the validity of rooted staggered QCD--are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.