Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory

TL;DR

This study precisely measures the topological charge distribution in SU(3) Yang--Mills theory, detecting non-Gaussian features and comparing results with theoretical models to understand quantum non-perturbative effects.

Contribution

It introduces a high-precision lattice computation of topological charge cumulants using a computationally efficient discretization method, confirming non-Gaussianity and consistency with large Nc predictions.

Findings

Topological susceptibility measured as t_0^2*chi=6.67(7)×10^-4

Ratio of fourth to second cumulant R=0.233(45)

Results support non-Gaussian, non-perturbative quantum fluctuations

Abstract

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.