AdS/CFT 4-point functions: How to succeed at z-integrals without really trying

TL;DR

The paper introduces a simplified method for computing AdS/CFT 4-point functions that avoids complex integrals, reproduces known results, and provides new calculations for massive vectors, especially relevant for AdS5xS5 supergravity.

Contribution

It presents a novel approach to evaluate exchange diagrams in AdS/CFT without needing the explicit bulk-to-bulk propagator, simplifying calculations for various fields.

Findings

Reproduces previous results for scalar, gauge boson, and graviton exchanges.

Provides new results for massive vector exchanges.

Shows that in AdS5xS5, exchange diagrams reduce to finite sums of scalar quartic graphs.

Abstract

A new method is discussed which vastly simplifies one of the two integrals over AdS(d+1) required to compute exchange graphs for 4-point functions of scalars in the AdS/CFT correspondence. The explicit form of the bulk-to-bulk propagator is not required. Previous results for scalar, gauge boson and graviton exchange are reproduced, and new results are given for massive vectors. It is found that precisely for the cases that occur in the AdS(5) X S(5) compactification of Type IIB supergravity, the exchange diagrams reduce to a finite sum of graphs with quartic scalar vertices. The analogous integrals in n-point scalar diagrams for n>4 are also evaluated.