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We present a precise computation of the topological susceptibility$\chi_{_\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. Thecomputation is done on the lattice, using high-statistics Monte Carlosimulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two majorimprovements make it possible to go to finer lattice spacing and larger $N$compared to previous works. First, the topological charge is implementedthrough the gradient flow definition; and second, open boundary conditions inthe time direction are employed in order to avoid the freezing of thetopological charge. The results allow us to extrapolate the dimensionlessquantity $t_0^2\chi_{_\mathrm{YM}}$ to the continuum and large $N$ limits withconfidence. The accuracy of the final result represents a new quality in theverification of large $N$ scaling.

The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory