Spinning strings in AdS_3 x S^3 with NS-NS flux

TL;DR

This paper extends the integrable Neumann-Rosochatius system to describe spinning strings in AdS_3 x S^3 x T^4 with NS-NS flux, deriving energy-spin relations for specific rotating string solutions.

Contribution

It introduces an extended Neumann-Rosochatius model to incorporate NS-NS flux effects in spinning string solutions in AdS_3 x S^3 x T^4.

Findings

Derived energy dependence on spin and angular momenta for constant radii solutions.

Extended the integrable system to include NS-NS flux effects.

Provided explicit relations in the large 't Hooft coupling expansion.

Abstract

The sigma model describing closed strings rotating in AdS_3 x S^3 is known to reduce to the one-dimensional Neumann-Rosochatius integrable system. In this article we show that closed spinning strings in AdS_3 x S^3 x T^4 in the presence of NS-NS three-form flux can be described by an extension of the Neumann-Rosochatius system. We consider closed strings rotating with one spin in AdS_3 and two different angular momenta in S^3. For a class of solutions with constant radii we find the dependence of the classical energy on the spin and the angular momenta as an expansion in the square of the 't Hooft coupling of the theory.