Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

TL;DR

This paper investigates the IIB matrix model, a candidate for nonperturbative superstring theory, revealing spontaneous Lorentz invariance breaking from ten to at least eight dimensions through a saddle-point analysis.

Contribution

It introduces an integer deformation parameter to the IIB matrix model and analyzes its effects, showing spontaneous Lorentz symmetry breaking at large deformation.

Findings

Lorentz invariance is broken from 10D to at least 8D.

The deformed model remains well-defined and preserves key symmetries.

Further symmetry breaking is suggested but not yet confirmed.

Abstract

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.