Comment on: “Chiral anomalies and rooted staggered fermions” [Phys. Lett. B 649 (2007) 230]

Bérnard, C.; Golterman, Maarten; Shamir, Yigal; Sharpe, Stephen R.

doi:10.1016/j.physletb.2007.04.018

Cited by 53 publications

(86 citation statements)

References 35 publications

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“…It is straightforward to construct correlation functions that are contained in the physical sector of the RCT, and thus are free from unphysical effects. In the main text we used a projection onto a single taste, while in the Appendix we show how a different projection, used in our earlier paper [18], also works. For each of these approaches, there exist lattice versions that go over to the desired projections in the continuum limit and that can easily be applied to the rooted staggered theory.…”

Section: Discussionmentioning

confidence: 99%

“…This is explained in detail in Refs. [2,18]. If on the contrary, the chiral limit is taken first, while keeping a = 0, the finite-volume condensate will vanish [2,3].…”

Section: Ward Identitiesmentioning

confidence: 99%

“…If one is interested in mesonic observables only, another projection onto the physical sector of the RCT is available, which was discussed in detail previously [16,18]. In the Appendix, we use this projection to study the effects of 't Hooft vertices on mesonic correlation functions, arriving at the same final conclusions, namely that the physical sector of the RCT correctly reproduces one-flavor QCD.…”

Section: Rooted Correlation Functions In the Continuum Limitmentioning

confidence: 99%

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

et al. 2008

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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 also show that, due to the singular behavior of unphysical correlation functions as the massless limit is approached, order parameters for non-anomalous symmetries can be non-vanishing in finite volume if these symmetries act outside of the physical subspace. 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.

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Section: Discussionmentioning

confidence: 99%

“…This is explained in detail in Refs. [2,18]. If on the contrary, the chiral limit is taken first, while keeping a = 0, the finite-volume condensate will vanish [2,3].…”

Section: Ward Identitiesmentioning

confidence: 99%

Section: Rooted Correlation Functions In the Continuum Limitmentioning

confidence: 99%

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

et al. 2008

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“…Indeed, the main purpose of lattice gauge theory is to obtain non-perturbative information on field theories, and the 't Hooft interaction is one of the most important non-perturbative effects. Nevertheless, the large investments that have been made in such algorithms has led some authors to attempt refuting this flaw [7,9,10].…”

Section: Consequences For Rooted Determinantsmentioning

confidence: 99%

The ’t Hooft vertex revisited

Creutz

2008

Annals of Physics

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In 1976 't Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multifermion interaction. These old arguments provide a link between a variety of recent and sometimes controversial ideas including discrete chiral symmetries appearing in some models for unification, ambiguities in the definition of quark masses, and flaws with some simulation algorithms in lattice gauge theory.

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“…there is a mismatch between the (rooted) sea quarks and the (unrooted) valence quarks [6][7][8]. PQChPT plays an important role in the development of the effective chiral theory for rooted staggered fermions [9,10], which in turn provides some evidence for the validity of the rooting procedure.…”

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confidence: 99%

On the foundations of partially quenched chiral perturbation theory

Bérnard

Golterman

2013

Phys. Rev. D

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It has been widely assumed that partially quenched chiral perturbation theory is the correct lowenergy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa-Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.

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Comment on: “Chiral anomalies and rooted staggered fermions” [Phys. Lett. B 649 (2007) 230]

Cited by 53 publications

References 35 publications

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

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

The ’t Hooft vertex revisited

On the foundations of partially quenched chiral perturbation theory

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