Non-Gaussianity of the topological charge distribution in $\mathrm{SU}(3)$ Yang-Mills theory

TL;DR

This study investigates the non-Gaussian features of the topological charge distribution in SU(3) Yang-Mills theory by computing higher cumulants using gradient flow, providing precise continuum limit results.

Contribution

The paper proves the equivalence of lattice and continuum definitions of topological charge cumulants and presents high-precision numerical results for the second and fourth cumulants in SU(3) Yang-Mills theory.

Findings

Topological susceptibility measured as 6.67(7)×10^{-4} in units of t_0^2.

The ratio of the fourth to second cumulant is 0.233(45).

Results confirm non-Gaussianity of the topological charge distribution.

Abstract

In Yang-Mills theory, the cumulants of the na\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2\chi=6.67(7)\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.