Scaling, topological tunneling and actions for weak coupling DWF calculations

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.

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“…The advantage of open boundary conditions over periodic boundary conditions (see, however, ref. [22]) are illustrated in figure 1.…”

Section: Discussionmentioning

confidence: 99%

Topological susceptibility in lattice Yang-Mills theory with open boundary condition

Chowdhury

Harindranath

Maiti³

et al. 2014

J. High Energ. Phys.

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“…In the recent literature the problem of very long autocorrelation times and of the theoretical control over the systematic error in numerical simulations has been addressed in a series of papers [2,3,5,[7][8][9][10] and several solutions to the topological critical slowing down have been proposed [4,6,[19][20][21][22][23][24][25].…”

Section: Jhep07(2016)089mentioning

confidence: 99%

Metadynamics surfing on topology barriers: the CP N−1 case

Laio

Martinelli

Sanfilippo

2016

J. High Energ. Phys.

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As one approaches the continuum limit, QCD systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give biased results. The same is true in the case of two dimensional CP N −1 models. In this paper we show that metadynamics, when used to simulate CP N −1 , allows to address efficiently this problem. By studying CP 20 we show that we are able to reconstruct the free energy of the topological charge F (Q) and compute the topological susceptibility as a function of the coupling and of the volume. This is a very important physical quantity in studies of the dynamics of the θ vacuum and of the axion. This method can in principle be extended to QCD applications.

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“…Inspired by refs. [36,37], we tried, as an attempt, to enhance the number of configurations with nonzero Q by inserting…”

Section: Jhep10(2015)136mentioning

confidence: 99%

Topology in QCD and the axion abundance

Kitano

Yamada

2015

J. High Energ. Phys.

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The temperature dependence of the topological susceptibility in QCD, χ t , essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heatbath algorithm. We obtain an indication that unquenched calculations of χ t encounter the serious problem of autocorrelation already at T ∼ 2 T c or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of χ t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where χ t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.

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Scaling, topological tunneling and actions for weak coupling DWF calculations

Cited by 8 publications

References 14 publications

Topological susceptibility in lattice Yang-Mills theory with open boundary condition

Topological susceptibility in lattice Yang-Mills theory with open boundary condition

Metadynamics surfing on topology barriers: the CP N−1 case

Topology in QCD and the axion abundance

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