Scale setting for large-$N$ SUSY Yang-Mills on the lattice

TL;DR

This study investigates the large-$N$ limit of 4D supersymmetric Yang-Mills theory on the lattice, focusing on scale setting, Pfaffian positivity, and the relation between lattice spacing and couplings, confirming perturbative predictions.

Contribution

It provides a detailed lattice analysis of large-$N$ SUSY Yang-Mills, including scale setting, Pfaffian positivity, and the coupling dependence of lattice spacing, extending understanding of nonperturbative SUSY dynamics.

Findings

Pfaffian remains positive in simulations.

Lattice spacing determined consistently across observables.

Dependence of lattice spacing on couplings matches perturbative predictions.

Abstract

In this paper we study the large $N$ limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice 't Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theory.