Giant magnons and spiky strings on the conifold

TL;DR

This paper derives explicit solutions for giant magnons and spiky strings on a squashed three-sphere, revealing new dispersion relations on the conifold that depend transcendently on energy and momenta.

Contribution

It provides explicit string solutions on the conifold and uncovers a novel transcendental dispersion relation linking energy and momenta.

Findings

Solutions describe strings on the conifold and squashed spheres.

Dispersion relations involve transcendental functions.

Special squashing parameters recover known sphere results.

Abstract

We find explicit solutions for giant magnons and spiky strings on the squashed three dimensional sphere. For a special value of the squashing parameter the solutions describe strings moving in a sector of the conifold, while for another value of the squashing parameter we recover the known results on the round three dimensional sphere. A new feature is that the energy and the momenta enter in the dispersion relation of the conifold in a transcendental way.