On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings

TL;DR

This paper investigates Lorentz symmetry breaking in a 4D matrix model related to superstring theories, finding no evidence of spontaneous symmetry breaking in simulations, highlighting the importance of fermionic phase effects in higher dimensions.

Contribution

It provides a detailed analysis of symmetry breaking in a 4D matrix model and emphasizes the role of fermionic phases in the potential spontaneous Lorentz symmetry breaking in 10D models.

Findings

No sign of SSB in Monte Carlo simulations with N up to 48

Moment of inertia suggests SSB, but Wilson loops do not confirm it

Fermionic phase is crucial for SSB in higher-dimensional models

Abstract

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas, Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D IIB matrix model.