Three-point correlators: Finite-size giant magnons and singlet scalar operators on higher string levels

In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to “heavy” string states, while the third vertex corresponds to a “light” state. This is done for the case when the “heavy” string states are finite-size giant magnons, carrying one or two angular momenta. The “light” states are taken to be singlet scalar operators on higher string levels. We first consider the case of string theory on AdS5×S5 dual to N=4 super Yang-Mills. Then we extend the obtained results to the γ-deformed AdS5×Sγ5, corresponding to N=1 super Yang-Mills theory, appearing as an exactly marginal deformation of N=4 super Yang-Mills.