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.
To investigate the properties of the large limit of N = 1 SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the adjoint-fermion one is the Wilson-Dirac action on a reduced lattice with twisted gauge boundary condition. We employ the RHMC algorithm in which the absolute value of the Pfaffian is incorporated. The sign of the Pfaffian is included with the re-weighting method and separately measured as an observable. In this talk, we show the configuration generation status towards the large limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Dirac adjoint fermion operator. We investigated the sign of the Pfaffian and the critical hopping parameters for the chiral limit. The sign of the Pfaffian is always positive on the configurations we have generated. The critical hopping parameters derived from the eigenvalues of the Dirac operator are consistent with those derived from the PCAC mass relation with non-singlet flavor adjoint fermions.
N = 1 SUSY Yang-Mills theory is an appealing theoretical framework that has been studied in the literature using different methods, including standard lattice simulations. Among these, the volume-reduced twisted Eguchi-Kawai model, endowed with one adjoint Majorana fermion, could play an important role in studying its large-limit via the Curci-Veneziano prescription. In this talk, we present our results on the analysis of the scale of the theory, performed via different methods based on purely gluonic observables as well as (quenched) fundamental mesons in the chiral limit. These lattice results will be used as a scale setting for the analysis of the spectrum of the theory.
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