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

TL;DR

We address the challenge of computing tree-level AdS/CFT correlators by embedding AdS physics in a higher-dimensional embedding space and recasting Witten diagrams in Mellin space. The authors develop an iterative sewing procedure that builds $N$-point amplitudes from lower-point off-shell components, expressing both scalar and vector correlators through shared Mellin amplitudes and Mandelstam variables $\delta_{ij}$. They provide explicit $3$-, $4$-, and $5$-point results and outline a general recursion for higher-point amplitudes, with careful treatment of vector index structures via $D_{MA}$ and related identities. This framework offers a systematic, potentially spin-extended route toward general Feynman rules for Witten diagrams with applications to higher-spin correlators and holographic computations.

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.

Figures (8)

• Figure 1: The three-point scalar amplitude \ref{['eqn8']}.
• Figure 2: The three-point vector amplitude \ref{['eq20']}.
• Figure 3: The four-point scalar amplitude \ref{['eqA4s0']}.
• Figure 4: The four-point vector amplitude \ref{['eq20c']}.
• Figure 5: The four-point vector amplitude \ref{['eq57o']}.