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We develop a general method of computing the contribution of the vertexoperators to the semi-classical correlation functions of heavy string states,based on the state-operator correspondence and the integrable structure of thesystem. Our method requires only the knowledge of the local behavior of thesaddle point configuration around each vertex insertion point and can beapplied to cases where the precise forms of the vertex operators are not known.As an important application, we compute the contributions of the vertexoperators to the three-point functions of the large spin limit of theGubser-Klebanov-Polyakov (GKP) strings in $AdS_3$ spacetime, left unevaluatedin our previous work [arXiv:1110.3949] which initiated such a study. Combiningwith the finite part of the action already computed previously and with thenewly evaluated divergent part of the action, we obtain finite three-pointfunctions with the expected dependence of the target space boundary coordinateson the dilatation charge and the spin.

Wave functions and correlation functions for GKP strings from integrability