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To investigate the properties of the large $N$ limit of $\mathcal{N} = 1$SUSY Yang-Mills theory, we have started a study for a reduced matrix model withan adjoint Majorana fermion. The gauge action is based on the Wilson action andthe adjoint-fermion one is the Wilson-Dirac action on a reduced lattice withtwisted gauge boundary condition. We employ the RHMC algorithm in which theabsolute value of the Pfaffian is incorporated. The sign of the Pfaffian isincluded with the re-weighting method and separately measured as an observable.In this talk, we show the configuration generation status towards the large $N$limit and the behavior of the lowest/lower eigenvalue(s) of the Wilson-Diracadjoint fermion operator. We investigated the sign of the Pfaffian and thecritical hopping parameters for the chiral limit. The sign of the Pfaffian isalways positive on the configurations we have generated. The critical hoppingparameters derived from the eigenvalues of the Dirac operator are consistentwith those derived from the PCAC mass relation with non-singlet flavor adjointfermions.

Large $N$ simulation of the twisted reduced matrix model with an adjoint Majorana fermion