Giant Magnons and Singular Curves

TL;DR

This paper derives giant magnon solutions in string theory from elliptic finite-gap solutions by degenerating spectral curves into singular curves, providing an alternative mathematical description linked to previous condensate cut methods.

Contribution

It introduces a novel approach to describe giant magnons as finite-gap solutions associated with singular spectral curves, connecting to existing condensate cut frameworks.

Findings

Derived giant magnon solutions from singular spectral curves.

Established a symplectic transformation linking different descriptions.

Provided an alternative mathematical framework for giant magnons.

Abstract

We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by degenerating its elliptic spectral curve into a singular curve. This alternate description of giant magnons as finite-gap solutions associated to singular curves is related through a symplectic transformation to their already established description in terms of condensate cuts developed in hep-th/0606145.