Three-point correlation function of giant magnons in the Lunin-Maldacena background

We compute semiclassical three-point correlation function, or structure constant, of two finite-size (dyonic) giant magnon string states and a light dilaton mode in the Lunin-Maldacena background, which is the γ-deformed, or TsT-transformed AdS ₅×Sγ5, dual to N=1 super Yang-Mills theory in four dimensions. We also prove that an important relation between the structure constant and the conformal dimension, checked for the N=4 super Yang-Mills case, still holds for the γ-deformed string background.