Miguel Francisco Garcia Vera (NIC, DESY & Humboldt Universitat zu Berlin)
We present a precise computation of the topological susceptibility $\chi$ of SU($N$) Yang–Mills theory in the large-$N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations of the SU($N$) Yang-Mills theories, with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements allowed us to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. Our results allow us to extrapolate the dimensionless quantity $t_0^2\chi$ to the continuum and large-$N$ limits with confidence. The accuracy of our final result represents a new quality in the verification of large-$N$ scaling.