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

TL;DR

This study explores the large N limit of supersymmetric Yang-Mills theory using a twisted reduced matrix model with adjoint Majorana fermions, employing advanced algorithms to analyze eigenvalues and Pfaffian signs.

Contribution

It introduces a simulation framework for the large N limit of SUSY Yang-Mills with adjoint fermions using twisted reduced models and RHMC algorithm, including Pfaffian sign measurement.

Findings

Pfaffian sign remains positive in generated configurations.

Critical hopping parameters align with PCAC mass estimates.

Eigenvalues indicate behavior consistent with chiral limit expectations.

Abstract

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 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 $N$ 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.