String Theory and Noncommutative Geometry

TL;DR

This paper explores how string theory with a B-field leads to noncommutative gauge theories, establishing an equivalence with ordinary gauge theories and examining implications for dualities and M-theory.

Contribution

It demonstrates an explicit change of variables connecting ordinary and noncommutative gauge fields, extending the understanding of noncommutative geometry in string theory.

Findings

Equivalence between noncommutative and ordinary gauge theories established.

Comparison of Dirac-Born-Infeld and noncommutative gauge actions.

Insights into T-duality, Morita equivalence, and noncommutative M-theory.

Abstract

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.