An HHL 3-point correlation function in the η-deformed AdS5 × S5

We derive the 3-point correlation function between two giant magnons heavy string states and the light dilaton operator with zero momentum in the η  -deformed AdS5×S5AdS5×S5 valid for any J1J1 and η   in the semiclassical limit. We show that this result satisfies a consistency relation between the 3-point correlation function and the conformal dimension of the giant magnon. We also provide a leading finite J1J1 correction explicitly.