It is well known that Yang-Mills theory possesses a nontrivial topological structure: it has an innite series of energetically degenerate but topologically distinct classical vacua. At nite temperature thermal uctuations of elds can lead to (sphaleron) transitions between various vacuums. Due to the chiral anomaly the rate of these transitions describes the evolution of the chiral charge in Quantum Chromodynamics or baryon charge in electroweak theory.
 For the rst time the sphaleron rate $\Gamma$ was measured by means of lattice simulations in gluodynamics with gauge group SU(3). Calculations are carried out on the basis of Kubo formula, which relates the sphaleron rate and correlator of the topological charge density. Topological charge density correlator was measured by Gradient Flow method. The inversion of the Kubo formula was carried out by Backus-Gilbert method. The nal result is $\Gamma/T^4=0.062(18)$ at the temperature $T/T_c=1.24$, what is in agreement with the results of real time calculations at weak coupling [1].

[1] G. D. Moore and M. Tassler, JHEP 1102, 105 (2011) doi:10.1007/JHEP02(2011)105 [arXiv:1011.1167 [hep-ph]].

A.Yu.Kotov

JETP Letters 108, issue 6 (2018)