Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$

Abstract

In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $\eta$ deformed $Ad{S}_5\times S^5$ 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 $\text{approximately}$ 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.

30 pages; references updated; version to appear in JHEP

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Cited by in corpus (7)

• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Chaotic spin chains in AdS/CFT
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• On pp wave limit for $\eta$ deformed superstrings
• An integrable deformed Landau-Lifshitz model with particle production?