Comments on Supersymmetric Yang-Mills Theory on a Noncommutative Torus

TL;DR

This paper investigates the relationship between supersymmetric Yang-Mills theory on a noncommutative torus and string theory, revealing that the Born-Infeld action remains relevant in the noncommutative limit.

Contribution

It demonstrates that the Born-Infeld action persists in the noncommutative torus limit, challenging the completeness of the usual supersymmetric Yang-Mills description.

Findings

Born-Infeld action survives the noncommutative limit

Supersymmetric Yang-Mills theory is not the complete description

Embedding D0-brane theory into string theory clarifies the dynamics

Abstract

D0-brane theory on a torus with a nonvanishing B field is embedded into a string theory in the weak coupling limit. It is shown that the usual supersymmetric Yang-Mills theory on a noncommutative torus can not be the whole story. The Born-Infeld action survives the noncommutative torus limit.