Nonperturbative determination of the $\mathcal{N}=1$ supersymmetric Yang-Mills gluino condensate at large $N$

We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{S}\mathrm{U}(N)$ Yang$-$Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-$N$ twisted volume reduction. We present two different determinations based, respectively, on the Banks$-$Casher formula and on the Gell-Mann$-$Oakes$-$Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov$-$Shifman$-$Vainshtein$-$Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the Renormalization Group Invariant (RGI) gluino condensate gives ${\mathrm{\Sigma }}_{\mathrm{R}\mathrm{G}\mathrm{I}}\mathrm{/}{\mathrm{\Lambda }}_{\mathrm{N}\mathrm{S}\mathrm{V}\mathrm{Z}}^3=[1.18(08{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(12{)}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}{]}^3=1.64(33{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(50{)}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}=1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach ${\mathrm{\Sigma }}_{\mathrm{R}\mathrm{G}\mathrm{I}}\mathrm{/}{\mathrm{\Lambda }}_{\mathrm{N}\mathrm{S}\mathrm{V}\mathrm{Z}}^3=1$.