Curved-space classical solutions of a massive supermatrix model

TL;DR

This paper explores a supermatrix model based on osp(1|32,R) that includes mass and cubic terms, revealing classical solutions that form noncommutative curved spaces, potentially relevant for M-theory.

Contribution

It introduces a massive supermatrix model with classical solutions forming noncommutative curved geometries, advancing understanding of matrix models related to M-theory.

Findings

Classical solutions form noncommutative curved spaces.

Solutions are energetically more favorable than trivial vacuum.

Explicit examples include fuzzy 2-spheres and fuzzy 8-sphere.

Abstract

We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(1|32,R), which could play a role in the construction of the eleven-dimensional M-theory. This model contains a massive version of the IIB matrix model, where some fields have a tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable. However, this model possesses several classical solutions where these fields build noncommutative curved spaces and these solutions are shown to be energetically more favorable than the trivial vacuum. In particular, we describe in details two cases, the SO(3) \times SO(3) \times SO(3) (three fuzzy 2-spheres) and the SO(9) (fuzzy 8-sphere) classical backgrounds.