Scattering of single spikes

TL;DR

This paper uses the dressing method to construct and analyze single spike string solutions on a three-sphere, including scattering behavior, revealing connections to integrable spin chains similar to giant magnons.

Contribution

It introduces a new application of the dressing method to single spike solutions and their scattering, linking these solutions to integrable spin chains.

Findings

Constructed single spike solutions using the dressing method.

Analyzed scattering phase shifts of two single spikes.

Found the scattering phase shift matches that of giant magnons, up to non-logarithmic terms.

Abstract

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and compute the scattering phase shift. As a function of the dressing parameters, the result is exactly the same as the one for the giant magnon, up to non-logarithmic terms. This suggests that the single spikes should be described by an integrable spin chain closely related to the one associated to the giant magnons. The field theory interpretation of such spin chain however is still unclear.