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

TL;DR

This paper reports the first nonperturbative large-N lattice calculation of the $ ext{SU}(N)$ supersymmetric Yang-Mills gluino condensate, comparing numerical results with analytic predictions and achieving consistent, precise measurements.

Contribution

It introduces a novel nonperturbative lattice approach using large-N volume reduction to compute the gluino condensate in $ ext{SU}(N)$ SYM, connecting numerical and analytic results.

Findings

Consistent results from two different determination methods.

First comparison of lattice results with NSVZ scheme predictions.

Accurate RGI gluino condensate value aligning with theoretical expectations.

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 $\Sigma_{\rm RGI} /\Lambda_{\rm NSVZ}^3 = [1.18\, (08)_{\rm stat}\, (12)_{\rm syst}]^3 = 1.64(33)_{\rm stat} \, (50)_{\rm syst} = 1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach $\Sigma_{\rm RGI} /\Lambda_{\rm NSVZ}^3 = 1$.