Topological matrix model

Abstract

Starting from the primal principle based on the noncommutative nature of (9 + 1)-dimensional spacetime, we construct a topologically twisted version of the supersymmetric reduced model with a certain modification. Our formulation automatically provides extra (1+1)-dimensions, thereby the dimension of spacetime is promoted to 10 + 2. With a suitable gauge choice, we can reduce the model with (10 + 2)-dimensional spacetime to the one with (9 + 1)-dimensions and thus we regard this gauge as the light-cone gauge. It is suggested that the model so obtained would describe the light-cone F-theory. From this viewpoint we argue the relation of the reduced model to the matrix model of M-theory and the SL(2, Z) symmetry of type IIB string theory. We also discuss the general covariance of the matrix model in a broken phase, and make some comments on the background independence.