Topological Matrix Model

TL;DR

This paper constructs a topologically twisted supersymmetric matrix model starting from noncommutative (9+1)-dimensional spacetime, leading to a (10+2)-dimensional framework that relates to F-theory, M-theory, and type IIB string theory.

Contribution

It introduces a novel topological matrix model with extra dimensions, connecting it to F-theory and exploring its symmetries and covariance properties.

Findings

Model naturally extends to 10+2 dimensions

Reduces to (9+1)-dimensional model via gauge choice

Suggests relation to light-cone F-theory and string dualities

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 dimensions of spacetime are 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.