Noncommutative D-Brane in Non-Constant NS-NS B Field Background

TL;DR

This paper explores how non-zero NS-NS B field strength leads to a new form of noncommutative geometry on D-branes, characterized by mixed commutation relations between coordinates and momenta, differing from the constant B field case.

Contribution

It introduces a novel noncommutative space arising from non-constant B field backgrounds, expanding the understanding of D-brane world volume geometries.

Findings

Coordinates and momenta satisfy mixed commutation relations.

New noncommutative space structure identified.

Differences from constant B field case demonstrated.

Abstract

We show that when the field strength H of the NS-NS B field does not vanish, the coordinates X and momenta P of an open string endpoints satisfy a set of mixed commutation relations among themselves. Identifying X and P with the coordinates and derivatives of the D-brane world volume, we find a new type of noncommutative spaces which is very different from those associated with a constant B field background.