p-p' System with B Field and Projection Operator Noncommutative Solitons

TL;DR

This paper explores the behavior of noncommutative solitons in a D-brane system with a background B field, analyzing scattering amplitudes to reveal the role of projection operators onto various states.

Contribution

It demonstrates how projection operators onto excited states naturally appear in scattering amplitudes within noncommutative D-brane systems with background B fields.

Findings

Projection operators onto higher excited states emerge in amplitudes.

Weyl transform of projection operators appears as multiplicative factors.

Analysis clarifies Dp-brane perception from Dp'-brane worldvolume theory.

Abstract

We study the system of the Dp'-brane with Dp-brane (p<p') inside, in the case where B_{ij} field is a nonvanishing constant. In order to understand how the Dp-brane is viewed from the Dp'-brane worldvolume theory, we investigate the process in which the Dp-brane is probed with p'-p' open string. We calculate the scattering amplitudes among p-p' open strings and p'-p' open strings and show that not only the Weyl transform of the projection operator onto the ground state but also those onto higher excited states emerge as multiplicative factors of the amplitudes.