Comparison of different lattice definitions of the topological charge

Cichy, Krzysztof; Dromard, Arthur; García-Ramos, Elena; Ottnad, Konstantin; Urbach, Carsten; Wagner, Marc; Wenger, Urs; Zimmermann, Falk

doi:10.48550/arxiv.1411.1205

Cited by 15 publications

(18 citation statements)

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“…Possible alternatives may consist in choosing a different action to be minimized during the smoothing procedure, or in performing a continuous integration of the minimization equations. The latter procedure is known as the gradient flow [45,46] and has been shown to provide results equivalent to cooling regarding topology [47][48][49][50]. Because of its computational simplicity in this work we will thus use cooling, however it will be interesting to consider in future studies also the gradient flow, especially as an independent way to fix the physical scale [46,51,52].…”

Section: Determination Of the Topological Contentmentioning

confidence: 99%

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

Bonati

D’Elia

Mariti

et al. 2016

J. High Energ. Phys.

180

218

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We investigate the topological properties of N f = 2 + 1 QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings a ∼ 0.05− 0.12 fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility χ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from T c up to around 4 T c , where we provide continuum extrapolated results for the topological susceptibility and for the fourth moment of the topological charge distribution. While the latter converges to the dilute instanton gas prediction the former differs strongly both in the size and in the temperature dependence. This results in a shift of the axion dark matter window of almost one order of magnitude with respect to the instanton computation.

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Section: Determination Of the Topological Contentmentioning

confidence: 99%

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

Bonati

D’Elia

Mariti

et al. 2016

J. High Energ. Phys.

180

218

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“…Gluonic definitions are typically affected by renormalizations related to fluctuations at the ultraviolet (UV) cutoff scale, which can be cured by a proper smoothing of gauge configurations. Cooling [29][30][31][32][33] is a standard procedure adopted to do that; recently the gradient flow [34,35] has been introduced, which has been shown to provide results equivalent to cooling, at least regarding topology [36][37][38][39].…”

Section: A Lattice Implementation and Topological Charge Definitionmentioning

confidence: 99%

θdependence inSU(3)Yang-Mills theory from analytic continuation

Bonati¹,

D’Elia²,

Scapellato³

2016

Phys. Rev. D

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We investigate the topological properties of the SU (3) pure gauge theory by performing numerical simulations at imaginary values of the θ parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of θ and exploiting analytic continuation, we determine the free energy density up to the sixth order in θ, f (θ,. That permits us to achieve determinations with improved accuracy, in particular for the higher order terms, with control over the continuum and the infinite volume extrapolations. We obtain b2 = −0.0216(15) and |b4| 4 × 10 −4 .

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“…Of course all these methods agree up to cut-off effects but it is only the spectral flow and the index of the overlap operator that give an integer result. We refer the reader to [12] for a critical comparison of all methods.…”

Section: Introductionmentioning

confidence: 99%

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

2015

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We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artefacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.

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Comparison of different lattice definitions of the topological charge

Cited by 15 publications

References 0 publications

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

θdependence inSU(3)Yang-Mills theory from analytic continuation

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

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