Spontaneous symmetry breaking in the BFSS model: Analytical results using the Gaussian expansion method

TL;DR

This paper uses the Gaussian expansion method to analytically demonstrate spontaneous SO(9) symmetry breaking in the high-temperature BFSS matrix model, highlighting the crucial role of fermionic terms.

Contribution

It provides an analytical approach to show symmetry breaking in the BFSS model, emphasizing the importance of fermions, which was previously studied mainly numerically.

Findings

SO(9) symmetry is spontaneously broken at high temperature

Fermionic terms are essential for symmetry breaking

Bosonic case does not exhibit symmetry breaking

Abstract

We apply the Gaussian expansion method to the BFSS matrix model in the high temperature limit. When the (Euclidean) BFSS action is expanded about a Gaussian ansatz, it is shown that the SO(9) symmetry is spontaneously broken, analogous to what happens in the IKKT model. The analysis of the free energy, using the set of gap equations which determines the width of the Gaussian terms, is sufficient to show that this symmetry breaking happens only when the fermionic terms are included and is absent in the bosonic case.