Three-point correlation functions of giant magnons with finite size

We compute holographic three-point correlation functions or structure constants of a zero-momentum dilaton operator and two (dyonic) giant magnon string states with a finite-size length in the semiclassical approximation. We show that the semiclassical structure constants match exactly with the three-point functions between two su(2) magnon single trace operators with finite size and the Lagrangian in the large ʼt Hooft coupling constant limit. A special limit J≫λ of our result is compared with the relevant result based on the Lüscher corrections.