Curved Superspaces and Local Supersymmetry in Supermatrix Model

TL;DR

This paper extends a matrix model framework to include supergravity, demonstrating that supercovariant derivatives and local supersymmetry can be represented within supermatrix models, reproducing key equations of supergravity.

Contribution

It introduces a supermatrix model formalism that encodes supergravity, integrating local supersymmetry into the matrix model's symmetry structure.

Findings

Supercovariant derivatives are expressed as supermatrices.

Local supersymmetry is incorporated as part of superunitary symmetry.

Einstein and Rarita-Schwinger equations are compatible with the supermatrix formalism.

Abstract

In a previous paper, we introduced a new interpretation of matrix models, in which any d-dimensional curved space can be realized in terms of d matrices, and the diffeomorphism and the local Lorentz symmetries are included in the ordinary unitary symmetry of the matrix model. Furthermore, we showed that the Einstein equation is naturally obtained, if we employ the standard form of the action, S=-tr([A_a,A_b][A^a,A^b])+.... In this paper, we extend this formalism to include supergravity. We show that the supercovariant derivatives on any d-dimensional curved space can be expressed in terms of d supermatrices, and the local supersymmetry can be regarded as a part of the superunitary symmetry. We further show that the Einstein and Rarita-Schwinger equations are compatible with the supermatrix generalization of the standard action.