D-branes and the Noncommutative Torus

TL;DR

This paper demonstrates that gauge theories on noncommutative tori naturally emerge in certain superstring compactifications, providing evidence for their consistency as quantum theories and linking them to M theory via D-branes.

Contribution

It offers a physical derivation of the connection between noncommutative torus compactifications and M theory, confirming the conjecture by Connes, Douglas, and Schwarz.

Findings

Gauge theories on noncommutative tori arise in superstring compactifications.

Provides evidence that these theories are well-defined quantum models.

Links noncommutative geometry with M theory through D-brane analysis.

Abstract

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory compactification on the noncommutative torus with M theory compactification with constant background three-form tensor field.