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

TL;DR

The paper analyzes 't Hooft vertices in rooted staggered QCD by treating rooted theories as partially quenched and identifying a physical subspace that reproduces ordinary QCD. It shows that in this physical sector, the expected bilinear 't Hooft vertex emerges correctly, while unphysical higher-order vertices arise only in unphysical correlators and cancel when projecting to the physical subsector, provided the continuum limit precedes the chiral limit. Ward identities for anomalous and non-anomalous symmetries are shown to be consistent within the enlarged theory, allowing nonzero order parameters in finite volume for non-anomalous symmetries. The results argue against Creutz’s criticisms by demonstrating that unphysical 't Hooft vertices do not obstruct taste-symmetry restoration in the continuum limit, thereby supporting the viability of rooted staggered fermions for nonperturbative QCD studies when limits are taken in the correct order.

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.