Spectrum of Dirac operator and role of winding number in QCD

Leutwyler, H.; Smilga, Andrei

doi:10.1103/physrevd.46.5607

Cited by 771 publications

(1,470 citation statements)

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“…This explicit breaking of chiral symmetry gives also rise to additive ultraviolet divergences which make the definition of the condensate ambiguous. The crucial observation here is that the ultraviolet divergences are independent on the volume V and, in a regularization that preserves chiral symmetry, their magnitude is suppressed by a factor 1/V with respect to the contributions from the long-range correlations [18]. At any given lattice spacing the value of Σ can then be extracted with arbitrary precision from a finite-size scaling study of the condensate if the volumes are large enough.…”

Section: Jhep04(2007)090mentioning

confidence: 98%

“…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%

“…Smilga sum rule [18]. Eventually we extract the value of the low-energy constant Σ by matching the chiral effective theory formulas with the lattice results.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

“…breaking in infinite volume [17,18,39]. It is due to the long-range correlations left in the system at finite volume.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

“…The functional form of the condensate Σ ν (µ) is known for arbitrary values of µ ≤ 1 [18,42]. The condensate is also known in a partially quenched chiral effective theory with N f flavors and an extra valence one of massm v .…”

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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Section: Jhep04(2007)090mentioning

confidence: 98%

Section: Jhep04(2007)090mentioning

confidence: 99%

“…Smilga sum rule [18]. Eventually we extract the value of the low-energy constant Σ by matching the chiral effective theory formulas with the lattice results.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

“…breaking in infinite volume [17,18,39]. It is due to the long-range correlations left in the system at finite volume.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

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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Optimised Dirac operators on the lattice: construction, properties and applications

Bietenholz

2008

Fortschritte der Physik

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We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the -regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian -the chiral condensate and the pion decay constant -from QCD simulations with extremely light quarks. Motivation and overviewOver the recent decades quantum field theory has been established as the appropriate formalism for particle physics, as far as it is explored experimentally. Its treatment by perturbation theory led to successful results, for instance in Quantum Electrodynamics (QED), in the electroweak sector of the Standard Model and in Quantum Chromodynamics (QCD) at high energy. However, there are still many open questions, which require results at finite coupling strength -beyond the range of perturbation theory -such as numerous aspects of QCD at low and moderate energy.A method is known which has the potential to provide fully non-perturbative results for a number of field theoretic questions. This method applies Monte Carlo simulations to lattice regularised quantum field theories. The generic uncertainty of perturbation theory -uncontrolled contributions beyond the calculated order -disappears in this approach. However, one has to deal with statistical errors, as well as ambiguities in the extrapolation to the continuum and to a large volume.Simulation results are obtained at finite lattice spacing, which causes systematic artifacts in the numerically measured observables. The stability of dimensionless ratios of observables under the variation of the lattice spacing is denoted as the scaling behaviour. Its quality, which is vital for the reliability of the continuum extrapolation, depends on the way in which the lattice regularisation is implemented. This work deals * www.fp-journal.org Fortschr. Phys. 56, No. 2 (2008) 109For practical applications, i.e. for the applicability in simulations, the couplings have to be truncated. In Sect. 6 we describe our truncation scheme for the perfect fermion to a so-called hypercube fermion, which has been simulate...

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Generalized Thirring Models

Sachs

Wipf

1996

Annals of Physics

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The Thirring model and various generalizations of it are analyzed in detail. The four-Fermi interaction modifies the equation of state. Chemical potentials and twisted boundary conditions both result in complex fermionic determinants which are analyzed. The non-minimal coupling to gravity does deform the conformal algebra which in particular contains the minimal models. We compute the central charges, conformal weights and finite size effects. For the gauged model we derive the partition functions and the explicit expression for the chiral condensate at finite temperature and curvature. The Bosonization in compact curved space-times is also investigated.Comment: LaTex 55 pages, 2 figures, extended version of our previous work (hep-th/9308067

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Spectrum of Dirac operator and role of winding number in QCD

Cited by 771 publications

References 60 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

Optimised Dirac operators on the lattice: construction, properties and applications

Generalized Thirring Models

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