Matrix Theory in a Constant C Field Background

TL;DR

This paper explores how D0-branes in a constant C field are described by a supersymmetric matrix model, revealing connections to noncommutative super Yang-Mills theory and discussing the effects of various C field components.

Contribution

It introduces a matrix model description of D0-branes in a constant C field, highlighting the role of similarity transformations and their singularities, and links to noncommutative gauge theories.

Findings

Matrix model describes D0-branes in C field background.

Noncommutative super Yang-Mills emerges for specific C components.

Singular similarity transformations affect the theory's formulation.

Abstract

D0-branes moving in a constant antisymmetric C field are found to be described by quantum mechanics of the supersymmetric matrix model with a similarity transformation. Sometimes this similarity transformation is singular or ill-defined and cannot be ignored. As an example, when there are non-vanishing C_{-ij} components, we obtain the theory for Dp-branes which is effectively the noncommutative super Yang-Mills theory. We also briefly discuss the effects of other non-vanishing components such as C_{+ij} and C_{ijk}.