Single spike solutions for strings on S2 and S3

TL;DR

This paper investigates special solutions for rigidly rotating strings on S2 and S3, focusing on the novel single spike solution characterized by a spike pointing toward the north pole, and explores their properties and interpretations.

Contribution

It introduces and analyzes the single spike solution on S2 and extends it to S3, providing new insights into string configurations and their spin chain interpretations.

Findings

Single spike solution characterized by a spike pointing north.

Energy and angular momentum relations for the solutions.

Connections to spin chain models like free fermions and Hubbard model.

Abstract

We study solutions for rigidly rotating strings on a two sphere. Among them we find two limiting cases that have a particular interest, one is the already known giant magnon and the other we call the single spike solution. The limiting behavior of this last solution is a string infinitely wrapped around the equator. It differs from that solution by the existence of a single spike of height theta that points toward the north pole. We study its properties and compute its energy E and angular momentum J as a function of theta. We further generalize the solution by adding one angular momentum to obtain a solution on S3. We find a spin chain interpretations of these results in terms of free fermions and the Hubbard model but the exact relation with the same models derived from the field theory is not clear.