Pulsating strings with mixed three-form flux

Abstract

Circular strings pulsating in AdS_(3) × S^(3) × T^(4) with mixed R–R and NS–NS three-form fluxes can be described by an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical model. In this article we find a general class of pulsating solutions to this integrable system that can be expressed in terms of elliptic functions. In the limit of strings moving in AdS_(3) with pure NS–NS three-form flux, where the action reduces to the SL(2, R) WZW model, we find agreement with the analysis of the classical solutions of the system performed using spectral flow by Maldacena and Ooguri. We use our elliptic solutions in AdS_(3) to extend the dispersion relation beyond the limit of pure NS–NS flux.