Towards 4-point correlation functions of any 1/2-BPS operators from supergravity

TL;DR

This paper simplifies the supergravity-derived effective action for 1/2-BPS operators, showing that complex four-derivative terms cancel out, supporting a conjecture about their four-point correlation functions in N=4 super Yang-Mills theory.

Contribution

It demonstrates the cancellation of four-derivative terms in the effective action, clarifying the structure of four-point functions for 1/2-BPS operators in supergravity.

Findings

Four-derivative terms in the effective action cancel out.

Supports the Mellin space conjecture for four-point functions.

Provides a simplified form of the effective action.

Abstract

The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S^5 is a starting point for computing the four-point correlation functions of arbitrary weight 1/2-BPS operators in N=4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S^5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any 1/2-BPS operators in the supergravity approximation.