A HHL 3-point correlation function in the \eta-deformed AdS_5 x S^5

TL;DR

This paper derives a three-point correlation function involving giant magnons and a dilaton operator in the ta-deformed AdS_5 x S^5, confirming consistency with conformal dimensions and providing finite J_1 corrections.

Contribution

It presents the first derivation of the 3-point function in the ta-deformed background for arbitrary J_1 and ta, including finite J_1 corrections.

Findings

The 3-point function satisfies a consistency relation with conformal dimensions.

Finite J_1 corrections are explicitly calculated.

The derivation applies to any J_1 and ta in the semiclassical limit.

Abstract

We derive the 3-point correlation function between two giant magnons heavy string states and the light dilaton operator with zero momentum in the \eta-deformed AdS_5 x S^5 valid for any J_1 and \eta 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 J_1 correction explicitly.