Elliptic solutions in the Neumann-Rosochatius system with mixed flux

TL;DR

This paper derives elliptic function solutions for spinning closed strings in AdS_3 x S^3 x T^4 with mixed fluxes, extending integrable system methods to include flux contributions and analyzing pure NS-NS flux limits.

Contribution

It extends the Neumann-Rosochatius integrable system to include flux effects and finds explicit elliptic solutions for spinning strings in mixed flux backgrounds.

Findings

Explicit elliptic solutions for spinning strings with mixed flux

Extended integrals of motion incorporating flux contributions

Exact energy expressions in pure NS-NS flux limit

Abstract

Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS three-form fluxes are described by a deformation of the one-dimensional Neumann-Rosochatius integrable system. In this article we find general solutions to this system that can be expressed in terms of elliptic functions. We consider closed strings rotating either in S^3 with two different angular momenta or in AdS_3 with one spin. In order to find the solutions we will need to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system to include the contribution from the flux. In the limit of pure NS-NS flux, where the problem can be described by a supersymmetric WZW model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.