Noncommutative Open String and D-brane

TL;DR

This paper demonstrates how quantizing open strings on D-branes with a background B field leads to noncommutative spacetime coordinates and D-brane worldvolumes, extending previous results and providing a string theory derivation.

Contribution

It introduces a string theory derivation of noncommutativity on D-branes with background B fields, generalizing prior Matrix model results for higher-dimensional branes.

Findings

Spacetime coordinates of string endpoints become noncommutative.

D-brane worldvolume exhibits noncommutativity due to background B field.

Results align with Matrix theory for p>=2 D-branes when A=0 and T-duality radii are considered.

Abstract

In this paper we consider the quantization of open strings ending on D-branes with a background B field. We find that spacetime coordinates of the open string end-points become noncommutative, and correspondingly the D-brane worldvolume also becomes noncommutative. This provides a string theory derivation and generalization of the noncommutativity obtained previously in the Matrix model compactification. For Dp-branes with p>=2 our results are new and agree with that of Matrix theory for the case of A=0 (where $A$ is the worldvolume gauge field) if the T-duality radii are used.