Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction

TL;DR

This paper systematically derives and classifies classical string solutions on RxS^2 related to elliptic sine-Gordon solutions, revealing their properties and connections to dual models within the AdS/CFT correspondence.

Contribution

It inverts Pohlmeyer reduction to classify and analyze elliptic string solutions, including well-known types, and explores their physical and duality properties.

Findings

Classified string solutions via Pohlmeyer reduction inversion.

Established correspondence between string spikes and sine-Gordon topological charge.

Derived closed-form dispersion relations for a broad class of solutions.

Abstract

We study classical string solutions on RxS^2 that correspond to elliptic solutions of the sine-Gordon equation. In this work, these solutions are systematically derived inverting Pohlmeyer reduction and classified with respect to their Pohlmeyer counterparts. These solutions include the spiky strings and other well-known solutions, such as the BMN particle, the GKP string or the giant magnons, which arise as special limits, and reveal many interesting features of the AdS/CFT correspondence. A mapping of the physical properties of the string solutions to those of their Pohlmeyer counterparts is established. An interesting element of this mapping is the correspondence of the number of spikes of the string to the topological charge in the sine-Gordon theory. In the context of the sine-Gordon/Thirring duality, the latter is mapped to the Thirring model fermion number, leading to a natural classification of the solutions to fermionic objects and bosonic condensates. Finally, the convenient parametrization of the solutions, enforced by the inversion of the Pohlmeyer reduction, facilitates the study of the string dispersion relation. This leads to the identification of an infinite set of trajectories in the moduli space of solutions, where the dispersion relation can be expressed in a closed form by means of some algebraic operations, arbitrarily far from the infinite size limit.