The quenched Eguchi-Kawai model

Bhanot, Gyan; Heller, Urs M.; Neuberger, Herbert

doi:10.1016/0370-2693(82)90106-x

Cited by 406 publications

(512 citation statements)

References 4 publications

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“…However, it is well-known that center symmetry does get broken in a small volume in the continuum limit: this can already be seen at the perturbative level, for all D > 2. In order to preserve center symmetry, various fixes have been proposed, since the 1980's: for example, in the quenched EK model [71], one studies the dynamics of the single-site model for a fixed set of eigenvalues of the link variables along the various directions, and then…”

Section: From Factorization To Orbifold Dualitiesmentioning

confidence: 99%

Introductory lectures to large- QCD phenomenology and lattice results

Lucini

Panero

2014

Progress in Particle and Nuclear Physics

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Section: From Factorization To Orbifold Dualitiesmentioning

confidence: 99%

Introductory lectures to large- QCD phenomenology and lattice results

Lucini

Panero

2014

Progress in Particle and Nuclear Physics

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“…It was shown that Wilson loop amplitudes do not depend on space-time and can be obtained from a single plaquette integral. However, this reduction is not valid in the weak coupling limit [10]. The idea of induced QCD [8] is to induce the plaquette action by a unitary matrix integral.…”

Section: Introductionmentioning

confidence: 99%

Qcd, Chiral Random Matrix Theoryand Integrability

Verbaarschot

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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SummaryRandom Matrix Theory has been a unifying approach in physics and mathematics. In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview of QCD, its low-energy limit and the microscopic limit of the Dirac spectrum which, as we will see in the second lecture, can be described by chiral Random Matrix Theory. The main topic of the third lecture is the recent developments on the relation between the QCD partition function and integrable hierarchies (in our case the Toda lattice hierarchy). This is an efficient way to obtain the QCD Dirac spectrum from the low energy limit of the QCD partition function. Finally, we will discuss the QCD Dirac spectrum at nonzero chemical potential. We will show that the microscopic spectral density is given by the replica limit of the Toda lattice equation. Recent results by Osborn on the Dirac spectrum of full QCD will be discussed.

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“…For the reduction to work the eigenvalues a i must be distributed more or less uniformly over a fairly large interval, larger than any physical mass scale in the problem. This is not the case in the simplest Eguchi-Kawai model, where the eigenvalues tend to clump around zero at weak coupling [7]. The problem can be circumvented in models with adjoint matter and/or double-trace couplings [14,15].…”

Section: Jhep06(2014)030mentioning

confidence: 99%

“…It can be shown that color averaging is equivalent to momentum integration to any order of planar perturbation theory [9], provided that the distribution ρ(a) is sufficiently flat. A well-known obstacle to Eguchi-Kawai reduction is that ρ(a), in principle a dynamical quantity, is not really flat [7]. For the reduction to work the eigenvalues a i must be distributed more or less uniformly over a fairly large interval, larger than any physical mass scale in the problem.…”

Section: Jhep06(2014)030mentioning

confidence: 99%