World Volume Noncommutativity versus Target Space Noncommutativity

TL;DR

This paper explores the dual roles of world volume and target space noncommutativity in D-branes, clarifying their relationship and constructing a boundary state on a noncommutative torus.

Contribution

It explicitly demonstrates the dual nature of noncommutativity in D-branes and constructs a boundary state on a noncommutative torus, revealing parameter relations.

Findings

Target space noncommutativity relates to conjugate momenta structure.

World volume noncommutativity relates to coordinate structure.

Explicit boundary state construction on noncommutative torus.

Abstract

It is known that the noncommutativity of D-brane coordinate is responsible for describing the higher-dimensional D-branes in terms of more fundamental ones such as D-particles or D-instantons, while considering a noncommutative torus as a target space is conjectured to be equivalent to introducing the background antisymmetric tensor field in matrix models. In the present paper we clarify the dual nature of both descriptions. Namely the noncommutativity of conjugate momenta of the D-brane coordinates realizes the target space structure, whereas noncommutativity of the coordinates themselves realizes world volume structure. We explicitly construct a boundary state for the Dirichlet boundary condition where the string boundary is adhered to the D-brane on the noncommutative torus. There are non-trivial relations between the parameters appeared in the algebra of the coordinates and that of the momenta.