Tree-level Correlators of scalar and vector fields in AdS/CFT

TL;DR

This paper develops an iterative method using embedding formalism and Mellin transforms to compute tree-level correlators of scalar and vector fields in AdS/CFT, enabling explicit calculations of multi-point functions.

Contribution

It introduces a new iterative procedure for constructing correlators by sewing lower-point diagrams, expressed in Mellin amplitudes, advancing computational techniques in AdS/CFT.

Findings

Explicit three-, four-, and five-point correlators calculated.

Scalar and vector correlators expressed in Mellin amplitudes.

Method generalizes to higher-point functions.

Abstract

Extending earlier results by Paulos, we discuss further the use of the embedding formalism and Mellin transform in the calculation of tree-level correlators of scalar and vector fields in AdS/CFT. We present an iterative procedure that builds amplitudes by sewing together lower-point off-shell diagrams. Both scalar and vector correlators are shown to be given in terms of Mellin amplitudes. We apply the procedure to the explicit calculation of three-, four- and five-point correlators.