Noncommutativity relations in type IIB theory and their supersymmetry

TL;DR

This paper explores how noncommutativity arises in D-brane world-volumes within type IIB superstring theory, revealing supersymmetry connections and the role of momenta in inducing noncommutative relations.

Contribution

It demonstrates that noncommutativity parameters form components of an N=1 supermultiplet and links boundary conditions to supersymmetry-preserving constraints.

Findings

Noncommutativity is induced by momenta at string endpoints.

Noncommutativity parameters are components of an N=1 supermultiplet.

Boundary conditions preserve half of the supersymmetry.

Abstract

In the present paper we investigate noncommutativity of $D9$ and $D5$-brane world-volumes embedded in space-time of type IIB superstring theory. Boundary conditions, which preserve half of the initial supersymmetry, are treated as canonical constraints. Solving the constraints we obtain original coordinates in terms of the effective coordinates and momenta. Presence of momenta induces noncommutativity of string endpoints. We show that noncommutativity relations are connected by N=1 supersymmetry transformations and noncommutativity parameters are components of N=1 supermultiplet.