Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice

Understand

We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory.

• It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow.
• The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method.
• We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility $\chi_t^\text{YM}$) and the fourth cumulant of the distribution.