The CFT_6 origin of all tree-level 4-point correlators in AdS_3 times S^3

Stefano Giusto,Alexander Tyukov,Congkao Wen,Rodolfo Russo

doi:10.1140/epjc/s10052-020-8300-4

Abstract

We provide strong evidence that all tree-level 4-point holographic correlators in hbox {AdS}_3 times S^3 are constrained by a hidden 6D conformal symmetry. This property has been discovered in the hbox {AdS}_5 times S^5 context and noticed in the tensor multiplet subsector of the AdS_3 times S^3 theory. Here we extend it to general AdS_3 times S^3 correlators which contain also the chiral primary operators of spin zero and one that sit in the gravity multiplet. The key observation is that the 6D conformal primary field associated with these operators is not a scalar but a self-dual 3-form primary. As an example, we focus on the correlators involving two fields in the tensor multiplets and two in the gravity multiplet and show that all such correlators are encoded in a conformal 6D correlator between two scalars and two self-dual 3-forms, which is determined by three functions of the cross ratios. We fix these three functions by comparing with the results of the simplest correlators derived from an explicit supergravity calculation.

Highlights

Possible to study explicitly a large class of correlators and to extracting interest CFT data such as couplings and anomalous dimensions [11,12]
We provide strong evidence that all tree-level 4point holographic correlators in AdS3 × S3 are constrained by a hidden 6D conformal symmetry
We focus on the correlators involving two fields in the tensor multiplets and two in the gravity multiplet and show that all such correlators are encoded in a conformal 6D correlator between two scalars and two self-dual 3-forms, which is determined by three functions of the cross ratios

Summary

Introduction

It has been noticed [14,15] that the holographic 4-point correlators in AdS3 × S3 duality share some key properties with the AdS5 cousin and so it is natural to ask whether a hidden conformal symmetry is present in this case. When focusing just on external states that are “matter” multiplets (i.e. tensor multiplet of the N = (2, 0) 6D supergravity), it was shown [14] that all 4-point holographic correlators derived in [14,15] can be obtained via a recursion relation from the lowest AdS3/CFT2 4-point correlator obtained in [18]. In order to obtain an explicit recursion relation one needs the results for some correlators which fix the initial data of the recursion We obtained these correlators by generalising the approach of [15]; here we will quote just the results we need and refer to a forthcoming paper [19] for their derivation. The framework presented in this work should make it possible to bring our knowledge of holographic correlators in AdS3 × S3 up to the same level as the AdS5 × S5 counterpart and start a systematic study of the OPE data in the gravity regime, an analysis of loop corrections and possibly of string corrections by adapting to AdS3 successful approaches in the AdS5 case [20,21,22,23,24,25,26,27,28,29,30,31,32]

Hints of a hidden 6D conformal symmetry

The CFT6 4-point correlator

A new recursion relation