Large-N SU(N) Yang-Mills theories with milder topological freezing

Bonanno, Claudio; Bonati, Claudio; D’Elia, Massimo

doi:10.1007/jhep03(2021)111

Cited by 44 publications

(49 citation statements)

References 73 publications

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“…The two are within errors as one would expect. We note that this value is consistent within errors with the N = ∞ extrapolation in [68] which uses a novel technique [69] for ameliorating the problem of topological freezing. Finally we return to the case of SU(3) since it also has some phenomenological interest.…”

Section: Topological Susceptibilitysupporting

confidence: 81%

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

Athenodorou

Teper

2021

J. High Energ. Phys.

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We calculate the low-lying glueball spectrum, several string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3 + 1 dimensions. We do so for 2 ≤ N ≤ 12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N = ∞. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k = 2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g2(a) ∝ 1/N for constant physics as N → ∞. We fit our calculated values of a√σ with the 3-loop β-function, and extract a value for $$ {\Lambda}_{\overline{MS}} $$ Λ MS ¯ , in units of the string tension, for all our values of N, including SU(3). We use these fits to provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N ≤ 6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(β), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice θ parameter. We provide quantitative results for how the topological charge ‘freezes’ with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and β, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.

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Section: Topological Susceptibilitysupporting

confidence: 81%

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

Athenodorou

Teper

2021

J. High Energ. Phys.

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“…Near the continuum limit, distinct topological sectors are poorly sampled due to the large energy barriers separating them, leading to exponentially increasing autocorrelation times as the continuum limit is approached in a finite volume. This problem has received a lot of attention, and several algorithmic strategies have been proposed over the years [5][6][7][8][9][10], but there is no fully satisfactory solution.…”

Section: Introductionmentioning

confidence: 99%

Topological sampling through windings

Albandea¹,

Hernández²,

Ramos³

et al. 2021

Eur. Phys. J. C

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We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

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“…In this respect, the adoption of the algorithm recently employed in large-( ) pure-gauge simulations in Ref. [38] is a possible direction that can be explored in the near future.…”

Section: Discussionmentioning

confidence: 99%

Topology in high-$T$ QCD via staggered spectral projectors

Athenodorou¹,

Bonanno²,

Bonati³

et al. 2021

Preprint

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We present preliminary lattice results for the topological susceptibility in high-= 2 + 1 QCD obtained discretizing this observable via spectral projectors on eigenmodes of the staggered operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the continuum scaling of the gluonic susceptibility at high , related to the choice of non-chiral fermions in the action.

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Large-N SU(N) Yang-Mills theories with milder topological freezing

Cited by 44 publications

References 73 publications

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

Topological sampling through windings

Topology in high-$T$ QCD via staggered spectral projectors

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