Exactly massless quarks on the lattice

Neuberger, Herbert

doi:10.1016/s0370-2693(97)01368-3

Cited by 1,376 publications

(1,596 citation statements)

References 20 publications

(24 reference statements)

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“…We consider QCD with N f ≥ 2 degenerate flavours regularized on an Euclidean lattice of spacing a with the standard plaquette gauge action and with the Neuberger-Dirac operator [32]. The latter (see appendix A for unexplained notations) satisfies the GinspargWilson relation [33] γ…”

Section: The Quark Condensate With Ginsparg-wilson Fermionsmentioning

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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Section: The Quark Condensate With Ginsparg-wilson Fermionsmentioning

confidence: 99%

“…The Jacobian of the transformation is non-trivial, and the chiral anomaly is recoveredà la Fujikawa [34 -36], with the topological charge density operator defined as [32,37,38]…”

Section: The Quark Condensate With Ginsparg-wilson Fermionsmentioning

confidence: 99%

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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“…This suggestion was considered infeasible in practice and the paper was essentially ignored until the late 1990ies, when it was realized that there are indeed possible realizations [9,10] of that concept. Eventually a lattice version of the chiral rotations was formulated [11] which leaves the massless lattice action, if obeying the Ginsparg-Wilson condition (GWC), invariant.…”

Section: The Ginsparg-wilson Conditionmentioning

confidence: 99%

“…The most prominent representative in the group of GW-type actions is the overlap Dirac operator [10]. The massless operator is an explicit construction,…”

Section: Fermion Speciesmentioning

confidence: 99%

The hadron spectrum from lattice QCD

Lang

2008

Progress in Particle and Nuclear Physics

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“…More recently, the overlap formalism [4], developed by Narayanan and Neuberger as a way to formulate chiral gauge theories on the lattice, has provided the ingredients for a lattice version of Dirac operator index theory when the base manifold (spacetime) is an even-dimensional torus. A lattice version of the index arose there as the fermionic topological charge of the lattice gauge field, and can be expressed as the index of the Overlap lattice Dirac operator, introduced in [5]. The fact that the overlap formulation successfully reproduces the global gauge anomaly and obstructions to the vanishing of local gauge anomalies [6,7,8,9,10] indicates that it should also lead to a lattice version of families index theory for the Dirac operator.…”

Section: Introductionmentioning

confidence: 99%

Families index theory for Overlap lattice Dirac operator. I

Adams¹

2002

Nuclear Physics B

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The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over evendimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finitedimensional lattice setting.

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Exactly massless quarks on the lattice

Cited by 1,376 publications

References 20 publications

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

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

The hadron spectrum from lattice QCD

Families index theory for Overlap lattice Dirac operator. I

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