Correspondence between Noncommutative Soliton and Open String/D-brane System via Gaussian Damping Factor

TL;DR

This paper establishes a connection between noncommutative solitons and open string/D-brane systems using Gaussian damping factors, showing how D-branes can be interpreted as noncommutative solitons with matching scattering amplitudes.

Contribution

It identifies the Gaussian damping factor as a form factor of Dp-branes and links it to noncommutative solitons, providing a new interpretation and matching string and effective field theory results.

Findings

Gaussian damping factor equals Fourier transform of noncommutative soliton

D-brane in zero slope limit identified with noncommutative soliton

Three and four point amplitudes from effective action match string calculations

Abstract

The gaussian damping factor (g.d.f.) and the new interaction vertex with the symplectic tensor are the characteristic properties of the N-point scalar-vector scattering amplitudes of the p-p' (p < p') open string system which realizes noncommutative geometry. The g.d.f. is here interpreted as a form factor of the Dp-brane by noncommutative U(1) current. Observing that the g.d.f. is in fact equal to the Fourier transform of the noncommutative projector soliton introduced by Gopakumar, Minwalla and Strominger, we further identify the Dp-brane in the zero slope limit with the noncommutative soliton state. It is shown that the g.d.f. depends only on the total momentum of N-2 incoming/outgoing photons in the zero slope limit. In the description of the low-energy effective action (LEEA) proposed before, this is shown to follow from the delta function propagator and the form of the initial/final wave functions in the soliton sector which resides in x^{m} m= p+1, ...p' dependent part of the scalar field \Phi(x^\mu, x^m). The three and four point amplitudes computed from LEEA agree with string calculation. We discuss related issues which are resummation/lifting of infinite degeneracy and conservation of momentum transverse to the Dp-brane.