Instantons from over-improved cooling

Pérez, Margarita Garcı́a; González-Arroyo, Antonio; Snippe, Jeroen; Baal, Pierre van

doi:10.1016/0550-3213(94)90631-9

Cited by 110 publications

(76 citation statements)

References 46 publications

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“…In Fig. 11 we provide density plots for the full correlation coefficient matrix c Q 1 ðn c ÞQ 2 ðτÞ for the Wilson and Symanzik tree-level improved actions obtained when the 3 From a semiclassical point of view [33], smoothing with the Iwasaki action prevents large instantons from shrinking to the UV scale, but it also forces small instantons (dislocations) with size relevant to the UV scale to expand and, thus, χ increases with the smoothing scale. According to Eq.…”

Section: Correlation Coefficientmentioning

confidence: 99%

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Topological charge using cooling and the gradient flow

2015

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The equivalence of cooling to the gradient flow when the cooling step n c and the continuous flow step of gradient flow τ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate n c and τ and show that the results for the topological charge become equivalent when rescaling τ ≃ n c =ð3 − 15c 1 Þ, where c 1 is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved, and the Iwasaki gauge actions to configurations produced with N f ¼ 2 þ 1 þ 1 twisted mass fermions. We compute the topological charge, its distribution, and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling τ ≃ n c =ð3 − 15c 1 Þ leads to equivalent results.

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Section: Correlation Coefficientmentioning

confidence: 99%

“…As one decreases λ, the gauge fields are expected to become larger modifying the gauge action as well. The lattice action can be written [23,33] Fig. 2 where we observe less changes in the value of Q.…”

Section: Perturbative Relation Between Cooling and The Gradient Flowmentioning

confidence: 99%

Topological charge using cooling and the gradient flow

2015

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“…If this is so, there is no reason to believe that the fermion method to measure topological charge has less artefacts than the geometrical one. The problem of dislocations is related to the gauge action, which is very poor at measuring the action of small sized objects carrying topological charge, and the sensible way to get rid of this problem is to improve the gauge action [11,12,13]. On the other hand, measuring topology through the counting of the small real eigenvalues (taking into account their chiralities) might be computationally more efficient.…”

Section: Lith For the Improved Actionmentioning

confidence: 99%

“…If this is confirmed in four dimensions, the problem of dislocations should be handled by improving the plaquette action [11,12,13] rather than by using a different integer definition of the topological charge. Any such definition is not sensitive to topological objects of size roughly of O(a), since a is the only cutoff scale in the problem.…”

Section: Introductionmentioning

confidence: 99%

The index theorem on the lattice with improved fermion actions

Hernández¹

1998

Nuclear Physics B

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We consider a Wilson-Dirac lattice operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and use the geometrical definition of topological charge. This is also confirmed in a numerical study of the quenched Schwinger model. These results suggest that integer definitions of the topological charge based on counting real modes of the Wilson operator are equivalent to the geometrical definition. The problem of exceptional configurations and the sign problem in simulations with an odd number of dynamical Wilson fermions are briefly discussed.

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“…Hence we need robust means to identify how the topology of the gauge field changes over time. In this study we use the naive continuum integral formula, 16) where the F µν is defined from a clover-type approximation [73] summing over the field strength components extracted from four neighboring plaquettes Instead of the matrix logarithm one may also use the simple relation…”

Section: Topological Charge On the Latticementioning

confidence: 99%

Non-Abelian chiral instabilities at high temperature on the lattice

Akamatsu

Rothkopf

Yamamoto

2016

J. High Energ. Phys.

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Abstract:We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous Langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density n 5 = n R − n L . Evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial n 5 , relevant in both early universe baryogenesis and relativistic heavy-ion collisions. The topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial n 5 and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.

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Instantons from over-improved cooling

Cited by 110 publications

References 46 publications

Topological charge using cooling and the gradient flow

Topological charge using cooling and the gradient flow

The index theorem on the lattice with improved fermion actions

Non-Abelian chiral instabilities at high temperature on the lattice

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