Monte Carlo Studies of the Dimensionally Reduced 4d SU(N) Super Yang-Mills Theory

TL;DR

This paper uses Monte Carlo simulations to study a supersymmetric matrix model derived from 4d SU(N) super Yang-Mills theory, revealing insights into its large N behavior, space-time emergence, and supersymmetry effects.

Contribution

It provides the first large N simulations of the supersymmetric model, confirming Eguchi-Kawai equivalence without quenching or twist, and explores the dynamical space-time structure.

Findings

Large N limit yields well-defined string amplitude operators

Eguchi-Kawai equivalence holds within a finite scale range

Simulations up to N=768 confirm theoretical predictions

Abstract

We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory. The model is well defined for finite N and it is found that the large N limit obtained by keeping g^2 N fixed gives rise to well defined operators which represent string amplitudes. The space-time structure which arises dynamically from the eigenvalues of the bosonic matrices is discussed, as well as the effect of supersymmetry on the dynamical properties of the model. Eguchi-Kawai equivalence of this model to ordinary gauge theory does hold within a finite range of scale. We report on new simulations of the bosonic model for N up to 768 that confirm this property, which comes as a surprise since no quenching or twist is introduced.