A note on oscillating strings in $AdS_3 \times S^3$ with mixed three-form fluxes

TL;DR

This paper investigates pulsating string solutions in the AdS3 x S3 background with mixed fluxes, deriving dispersion relations and analyzing the impact of flux types on string dynamics.

Contribution

It provides a detailed analysis of pulsating strings supported by mixed fluxes, including dispersion relations and the behavior in pure flux limits, highlighting integrability aspects.

Findings

Derived dispersion relations for small NS-NS flux

Analyzed string behavior in pure RR and NS-NS flux limits

Confirmed integrability of the background

Abstract

We present a detailed study of the pulsating string solutions in AdS3 x S3 supported by both RR and NS-NS fluxes. This background has recently been proved to be integrable. We find the dispersion relation between the energy, oscillation number and other conserved charges when the NS-NS flux turned on is small. We further discuss the fate of the string solutions in pure RR and NS-NS cases.