Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models

TL;DR

This paper uses Monte Carlo simulations to investigate spontaneous rotational symmetry breaking in six-dimensional super Yang-Mills matrix models, supporting previous findings and demonstrating the effectiveness of the factorization method in complex-action systems.

Contribution

First-principles Monte Carlo analysis of SSB in D=6 super Yang-Mills models, confirming earlier Gaussian expansion results and showcasing the factorization method's utility.

Findings

SSB occurs in D=6 super Yang-Mills models.

Results are consistent with Gaussian expansion method.

Demonstrates the factorization method's effectiveness in complex-action problems.

Abstract

It has long been speculated that the spontaneous symmetry breaking (SSB) of SO(D) occurs in matrix models obtained by dimensionally reducing super Yang-Mills theory in D=6,10 dimensions. In particular, the D=10 case corresponds to the IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory, and the SSB may correspond to the dynamical generation of four-dimensional space-time. Recently, it has been shown by using the Gaussian expansion method that the SSB indeed occurs for D=6 and D=10, and interesting nature of the SSB common to both cases has been suggested. Here we study the same issue from first principles by a Monte Carlo method in the D=6 case. In spite of a severe complex-action problem, the factorization method enables us to obtain various quantities associated with the SSB, which turn out to be consistent with the previous results obtained by the Gaussian expansion method. This also demonstrates the usefulness of the factorization method as a general approach to systems with the complex-action problem or the sign problem.