Holographic Four-Point Functions in the (2, 0) Theory

TL;DR

This paper develops a symmetry-based method to compute four-point correlators of one-half BPS operators in the (2,0) theory holographically, extending previous approaches and providing new results for specific operator weights.

Contribution

It introduces a novel symmetry-driven approach to calculate holographic four-point functions in eleven-dimensional supergravity, avoiding detailed supergravity action knowledge.

Findings

Computed new four-point correlators for weights k=3, 4

Extended position space methods from AdS5 to AdS7

Simplified Mellin space formulation of superconformal Ward identities

Abstract

We revisit the calculation of holographic correlators for eleven-dimensional supergravity on $AdS_7\times S^4$. Our methods rely entirely on symmetry and eschew detailed knowledge of the supergravity effective action. By an extension of the position space approach developed in [1, 2] for the $AdS_5\times S^5$ background, we compute four-point correlators of one-half BPS operators for identical weights $k=2, 3, 4$. The $k=2$ case corresponds to the four-point function of the stress-tensor multiplet, which was already known, while the other two cases are new. We also translate the problem in Mellin space, where the solution of the superconformal Ward identity takes a surprisingly simple form. We formulate an algebraic problem, whose (conjecturally unique) solution corresponds to the general one-half BPS four-point function.