Cubic couplings in D=6 N=4b supergravity on AdS_3\times S^3

TL;DR

This work derives the cubic effective action for the AdS$_3$ reduction of D=6 ${\mathcal N}=4b$ supergravity on $AdS_3\times S^3$, enabling AdS exchange calculations for four-point functions of chiral primaries in the dual CFT$_2$. By performing a KK reduction, diagonalizing the linearized equations for scalars, vectors, and symmetric tensors, and applying nonlinear field redefinitions, the authors obtain explicit cubic vertices among chiral primaries, vectors, and massive gravitons, including the behavior at extremality. They demonstrate the consistent truncation of the 3D theory to the graviton multiplet, discuss a possible partial truncation with the lowest-weight spin-\(\tfrac{1}{2}\) multiplet, and provide detailed expressions for the coupling coefficients in terms of KK data and harmonic integrals. Overall, the results clarify the structure of AdS$_3$ exchange diagrams and their imprint on protected CPO correlators in the boundary CFT$_2$, contributing to a deeper understanding of holography in this AdS$_3$/CFT$_2$ setting.

Abstract

We determine the AdS exchange diagrams needed for the computation of 4--point functions of chiral primary operators in the SCFT_2 dual to the D=6 N=4b supergravity on the AdS_3\times S^3 background and compute the corresponding cubic couplings. We also address the issue of consistent truncation.