Elliptic string solutions on $$\mathbb {R}\times \hbox {S}^2$$ R×S2 and their pohlmeyer reduction

Abstract

Abstract We study classical string solutions on $$\mathbb {R}\times \hbox {S}^2$$ R×S2 that correspond to elliptic solutions of the sine-Gordon equation. In this work, these solutions are systematically derived by inverting the Pohlmeyer reduction. 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 association of the number of spikes of the string to the topological charge in the sine-Gordon theory. Finally, the adopted parametrization of the solutions facilitates the identification of a dense subset of the moduli space of solutions, where the dispersion relation can be expressed in a closed form, arbitrarily far from the infinite size limit.