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Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
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Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
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We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the ratio of the forth cumulant over the second we obtain R=0.233(45). The latter is compatible with the expectations from the large Nc expansion, while it rules out the theta-behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum non-perturbative nature.
Forward citations
Cited by 6 Pith papers
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The topological susceptibility slope $\chi^\prime$ in the large-$N$ limit
First non-perturbative lattice determination of the Yang-Mills topological susceptibility slope χ' in the large-N limit using a novel algorithm to avoid topological freezing.
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The large-$N$ Yang--Mills $\Lambda$-parameter from step scaling
First non-asymptotic-scaling determination of the large-N Yang-Mills Λ-parameter yields √(8t₀)Λ_MS(N=∞) = 0.639(36).
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Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
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Renormalization Group Approach to Confinement
Derives α_S(μ) ≃ Λ_S²/μ² from a scale-invariant gluon condensate via gradient flow, reaching an infrared fixed point consistent with confinement.
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Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.
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Bounding statistical errors in lattice field theory simulations
Introduces bounds-based stopping criteria and automatic windowing for autocorrelation integrals to estimate statistical errors in lattice field theory Monte Carlo simulations.
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