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We consider the leading finite-size effects on some structure constants forthe $\eta$ - deformed $AdS_5\times S^5$ background in the framework of thesemiclassical approach. The leading finite-size corrections are derived for thecases when we have two heavy string states represented by giant magnons and fortwo different choices of the light states corresponding to dilaton operatorwith nonzero momentum and primary scalar operators. Since the dual field theoryis still unknown, the results obtained here must be considered as conjecturesor as predictions from the string theory side.

Semiclassical structure constants in the eta-deformed AdS_5 x S^5: Leading finite-size corrections