Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

TL;DR

This paper uses Monte Carlo simulations to study the large N behavior of a supersymmetric matrix model derived from 4D SU(N) super Yang-Mills theory, revealing insights into space-time structure, string amplitudes, and Eguchi-Kawai equivalence.

Contribution

It provides the first detailed numerical analysis of the large N dynamics of a supersymmetric reduced model, comparing supersymmetric and bosonic cases.

Findings

Space-time extent shows universal N-scaling.

String amplitude correlators exhibit nontrivial scaling.

Eguchi-Kawai equivalence holds within a finite scale range.

Abstract

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large N behavior of the space-time extent with the result obtained from a low energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a nontrivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.