On Three-point Functions in the AdS_4/CFT_3 Correspondence

TL;DR

This paper computes three-point functions in ABJM theory, generalizing determinant formulas and comparing heavy-light correlators with string theory predictions in the Frolov-Tseytlin limit.

Contribution

It extends determinant representations to ABJM theory and demonstrates agreement between field theory and string theory for heavy-light correlators.

Findings

Determinant formula generalization for ABJM three-point functions

Factorization into N=4 SYM correlation functions

Agreement with string theory in the Frolov-Tseytlin limit

Abstract

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.