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In this paper, considering the correspondence between spin chains and stringsigma 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, wefocus only on the bosonic part of the full superstring action and compute therelevant 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, thesigma model on $ \eta $ deformed $S^5$ could be $\textit{approximately}$thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spinchain model. We compute the energy for a certain class of spinning strings indeformed $S^5$ and we show that this energy can be mapped to that of a similarspinning string in the purely imaginary $\beta$ deformed background.

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