Spinning strings: $\lambda$-deformation and non-Abelian T-dual limit

TL;DR

This paper studies the effects of the $mbda$-deformation on spinning strings in a specific target space, revealing how deformation alters string energies and configurations, especially in the non-Abelian T-dual limit.

Contribution

It provides a detailed analysis of spinning strings in the $mbda$-deformed background, highlighting changes in string behavior and energy spectra compared to the undeformed and NATD limits.

Findings

Deformation increases the energy of spinning strings.

Enlarges the gap between folded and circular string energies.

Circular strings vanish in the NATD limit, with fast strings matching GKP dispersion.

Abstract

The simplest example of the $\lambda$-deformation connects the SU(2) Wess-Zumino-Witten model with the non-Abelian T-dual (NATD) of the SU(2) principal chiral model. We analyze spinning strings with one spin propagating through the $\lambda$-deformation of the target space of the interpolation. We show that the situation apart from the NATD limit parallels the undeformed case. We demonstrate that regular spinning strings are either folded or circular, and that nearly degenerate spinning strings are either nearly point-like, fast, or slow. The effects of the $\lambda$-deformation are both the overall increment of the energy of spinning strings and the enlargement of the gap between the energies of folded and circular strings. In the NATD limit, we prove that circular strings disappear and that fast strings realize the dispersion relation of Gubser-Klebanov-Polyakov strings.