The microscopic spectral density of the QCD Dirac operator

Damgaard, Poul H.; Osborn, James C.; Toublan, D.; Verbaarschot, J. J. M.

doi:10.1016/s0550-3213(99)00094-2

Cited by 182 publications

(259 citation statements)

References 59 publications

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“…[1], which do not take into account all the subtleties coming from the ghost sector, rather than the correct symmetries introduced in Refs. [17,19,23]. The subtleties do not affect the general argument.…”

Section: A Recapitulation Of Leutwyler's Argumentsmentioning

confidence: 93%

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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Section: A Recapitulation Of Leutwyler's Argumentsmentioning

confidence: 93%

On the foundations of partially quenched chiral perturbation theory

Bérnard

Golterman

2013

Phys. Rev. D

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“…For later convenience, a factor α −2 is included in the integral to improve its convergence at large eigenvalues. Evidently, the spectral density is proportional to the discontinuity across the cut, and so can be uniquely recovered from the resolvent if the latter is known [20,21]. For |z| <ᾱ, the resolvent may be expanded in a convergent power series,…”

Section: Resolvent and Moments Of The Spectral Densitymentioning

confidence: 99%

Stability of lattice QCD simulations and the thermodynamic limit

Debbio¹,

Giusti²,

Lüscher³

et al. 2006

J. High Energy Phys.

149

253

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We study the spectral gap of the Wilson-Dirac operator in two-flavour lattice QCD as a function of the lattice spacing a, the space-time volume V and the current-quark mass m. It turns out that the median of the probability distribution of the gap scales proportionally to m and that its width is practically equal to a/ √ V . In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD.

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“…It can be made ultraviolet finite with the very same renormalization constants and subtraction coefficients. On the other hand the chiral effective theory makes definite predictions, with no extra free parameters, for the topology dependence of the infrared contribution to condensate [18,22,23], predictions which can be directly tested against lattice QCD results.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

“…it is possible to extract the NLO effective theory predictionρ(λ) of the spectral density in presence of N f flavors [22,23]. This is the functional form that is expected to matcĥ ρ(λ) in eq.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

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Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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The microscopic spectral density of the QCD Dirac operator

Cited by 182 publications

References 59 publications

On the foundations of partially quenched chiral perturbation theory

On the foundations of partially quenched chiral perturbation theory

Stability of lattice QCD simulations and the thermodynamic limit

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

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