Spinning strings: λ-deformation and non-Abelian T-dual limit

The simplest example of the λ-deformation connects the <math altimg="si1.svg"><mrow><mi mathvariant="normal">SU</mi><mi mathvariant="normal">(</mi><mn mathvariant="normal">2</mn><mi mathvariant="normal">)</mi></mrow></math> Wess-Zumino-Witten model with the non-Abelian T-dual (NATD) of the <math altimg="si1.svg"><mrow><mi mathvariant="normal">SU</mi><mi mathvariant="normal">(</mi><mn mathvariant="normal">2</mn><mi mathvariant="normal">)</mi></mrow></math> principal chiral model. We analyze spinning strings with one spin propagating through the truncation of an S-dual embedding of the λ-deformation of the target space into type IIB supergravity. 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 λ-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.