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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×S5 valid for any J1 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 J1 correction explicitly

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