Curved Superspaces and Local Supersymmetry in Supermatrix Model

In a previous paper, we introduced a new interpretation of matrix models, inwhich any d-dimensional curved space can be realized in terms of d matrices,and the diffeomorphism and the local Lorentz symmetries are included in theordinary unitary symmetry of the matrix model. Furthermore, we showed that theEinstein equation is naturally obtained, if we employ the standard form of theaction, S=-tr([A_a,A_b][A^a,A^b])+.... In this paper, we extend this formalismto include supergravity. We show that the supercovariant derivatives on anyd-dimensional curved space can be expressed in terms of d supermatrices, andthe local supersymmetry can be regarded as a part of the superunitary symmetry.We further show that the Einstein and Rarita-Schwinger equations are compatiblewith the supermatrix generalization of the standard action.Comment: 23 pages, 1 figure, PTPTeX. Eqs. (2.18), (2.19) and related comments modifie