Supermatrix Models

TL;DR

This paper explores supermatrix models based on super Lie algebras, examining their supersymmetry, potential reductions to IIB matrix models, and the hidden diffeomorphism invariance in noncommutative gauge theories.

Contribution

It introduces and analyzes supermatrix models with super Lie algebras, extending the symmetry structures and exploring their relation to IIB matrix models.

Findings

Supersymmetry structures of supermatrix models are characterized.

Possible reductions to IIB matrix model are discussed.

Diffeomorphism invariance is identified as hidden in noncommutative gauge theories derived from these models.

Abstract

We investigate several matrix models based on super Lie algebras, osp(1|32,R), u(1|16,16) and gl(1|32,R). They are natural generalizations of IIB matrix model and were first proposed by Smolin. In particular, we study the supersymmetry structures of these models and discuss possible reductions to IIB matrix model. We also point out that diffeomorphism invariance is hidden in gauge theories on noncommutative space which are derived from matrix models. This symmetry is independent of the global SO(9,1) invariance in IIB matrix model and we report our trial to extend the global Lorentz invariance to local symmetry by introducing u(1|16,16) or gl(1|32,R) super Lie algebras.