Pulsating strings with mixed three-form flux

TL;DR

This paper derives elliptic function solutions for pulsating strings in a mixed flux background of $AdS_3 imes S^3 imes T^4$, extending known models and connecting to the $SL(2, ext{R})$ WZW framework.

Contribution

It introduces a general class of pulsating string solutions in mixed flux backgrounds, expressed via elliptic functions, and extends the dispersion relation beyond pure NS-NS flux.

Findings

Derived elliptic solutions for pulsating strings in mixed flux backgrounds.

Confirmed consistency with $SL(2, ext{R})$ WZW model in pure NS-NS limit.

Extended the dispersion relation for strings in $AdS_3$ with mixed flux.

Abstract

Circular strings pulsating in $AdS_3 \times S^3 \times T^4$ 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 $SL(2,\mathbb{R})$ 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.