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

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.

19 pages, revtex, shortened version to appear in Phys. Rev. D

References in corpus (28)

• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Staggered eigenvalue mimicry
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Scaling tests with dynamical overlap and rooted staggered fermions
• Observations on staggered fermions at non-zero lattice spacing
• Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$
• Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe
• Chiral anomalies and rooted staggered fermions
• Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach
• Actions for dynamical fermion simulations: are we ready to go?
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Effective field theories for QCD with rooted staggered fermions
• Comment on "Chiral anomalies and rooted staggered fermions"
• Breakdown of staggered fermions at nonzero chemical potential
• Lattice fermions with complex mass
• On the fourth root prescription for dynamical staggered fermions
• Locality with staggered fermions
• Algorithms for Lattice QCD with Dynamical Fermions
• Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory
• Validity of the Rooted Staggered Determinant in the continuum limit
• The author replies
• A simplified test of universality in Lattice QCD
• Power-counting theorem for staggered fermions
• Testing universality and the fractional power prescription for the staggered fermion determinant
• The fourth root of the Kogut-Susskind determinant via infinite component fields
• Mixed Action Simulations on Staggered Background; Interpretation and Result for the 2-flavor QCD Chiral Condensate
• Instanton-anti-instanton molecule with non-zero-modes of quarks included

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• Update of $|V_{cb}|$ from the $\bar{B}\to D^{\ast }\ell \bar{\nu }$ form factor at zero recoil with three-flavor lattice QCD
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• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• The 't Hooft vertex revisited
• Lattice determinations of the strong coupling
• On the foundations of partially quenched chiral perturbation theory
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• Comment on "'t Hooft vertices, partial quenching, and rooted staggered QCD"
• Propagator of the lattice domain wall fermion and the staggered fermion
• QCD thermodynamics on the lattice
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