Vibrating giant spikes and the large-winding sector

TL;DR

This paper analyzes the single spike string solution, related to giant magnons, calculating its modes, stability, and Hamiltonian, revealing it is non-supersymmetric and unstable with a specific excitation structure.

Contribution

It provides a detailed mode analysis of the single spike solution, identifying its non-supersymmetric nature and formulating its Hamiltonian with winding charge.

Findings

Single spike is non-supersymmetric.

The solution is unstable.

Hamiltonian involves winding charge instead of angular momentum.

Abstract

The single spike is a rigidly rotating classical string configuration closely related to the giant magnon. We calculate bosonic and fermionic modes of this solution, from which we see that it is not supersymmetric. It can be viewed as an excitation above a hoop of string wound around the equator, in the same sense that the magnon is an excitation above an orbiting point particle. We find the operator which plays the role of the Hamiltonian for this sector, which compared to the magnon's E-J has the angular momentum replaced by a winding charge. The single spike solution is unstable, and we use the modes to attempt a semi-classical computation of its lifetime.