Fast spinning strings on $ \eta $ deformed $ AdS_5 \times S^{5} $

TL;DR

This paper investigates fast spinning string solutions in eta-deformed AdS5 x S5, revealing a connection to anisotropic SU(3) spin chains and mapping energies to beta-deformed backgrounds.

Contribution

It introduces a novel analysis of bosonic spinning strings in eta-deformed backgrounds, linking sigma models to anisotropic spin chains and comparing energies across different deformations.

Findings

Sigma model approximates anisotropic SU(3) spin chain in the fast spinning limit.

Energy of spinning strings in eta-deformed S^5 maps to that in beta-deformed backgrounds.

Analysis focuses on bosonic sectors of the superstring action.

Abstract

In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $ \eta $ deformed $ AdS_5 \times S^{5} $ in the so called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both $(R \times S^{3})_{\eta} $ and $(R \times S^{5})_{\eta} $ models. The resulting system reveals that in the fast spinning limit, the sigma model on $ \eta $ deformed $S^5$ could be $\textit{approximately}$ thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed $S^5$ and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary $\beta$ deformed background.