Super Yang-Mills on the Noncomutative Torus

TL;DR

This paper explores noncommutative supersymmetric Yang-Mills theory on a quantum torus, providing explicit solutions, transformations, and discussing Morita equivalence in the context of matrix theory compactification.

Contribution

It offers explicit solutions and transformations for noncommutative Yang-Mills on a quantum torus, and discusses Morita equivalence in this setting.

Findings

Solutions for fundamental and adjoint sections on a twisted quantum torus

Explicit transformations connecting different representations

Discussion of Morita equivalence of C*-algebras in this context

Abstract

After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two different gauges. We also give explicit transformations connecting different representations which have appeared in the literature. Finally we discuss the more mathematical concept of Morita equivalence of C*-algebras as it applies to our specific case.