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

Abstract

We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{SU}(N)$ 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 ${\Sigma }_{\mathrm{RGI}}/{\Lambda }_{\mathrm{NSVZ}}^3=[1.18(08{)}_{\mathrm{stat}}(12{)}_{\mathrm{syst}}{]}^3=1.64(33{)}_{\mathrm{stat}}(50{)}_{\mathrm{syst}}=1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach ${\Sigma }_{\mathrm{RGI}}/{\Lambda }_{\mathrm{NSVZ}}^3=1$.

Comments: v2: 12 pages (7 main text + 5 appendices), 6 figures (3 main text + 3 appendices). Minor revision to the text, results and conclusions unchanged. Title slightly modifed to conform to APS conventions. Matches accepted version on PRD