Towards the higher point holographic momentum space amplitudes

TL;DR

The paper tackles the problem of computing higher-point momentum-space correlators for conserved vector currents in $AdS_4$ using tree-level Witten diagrams. It develops and applies a bulk perturbation theory framework in axial gauge, decomposing amplitudes into bulk-to-bulk and bulk-to-boundary propagators and evaluating radial and internal-momentum integrals via residues to obtain compact, explicit results. The authors present concrete, closed-form expressions for four- and five-point vector amplitudes and outline a strategy for six-point amplitudes, suggesting a scalable path to generic $n$-point functions. These momentum-space results provide detailed data for AdS/CFT current correlators and offer a complementary perspective to Mellin-space and recursion-based approaches, with potential implications for cosmology and higher-spin AdS/CFT studies.

Abstract

In this paper, we calculate higher point tree level vector amplitudes propagating in AdS$_4$. We use bulk perturbation theory to compute tree level Witten diagrams. We show that when these amplitudes are written in momentum space, they reduce to relatively simple expressions. We explicitly compute four and five point correlators and also sketch a general strategy to compute the full six-point correlators.

Figures (6)

• Figure 1: The three point vector amplitude.
• Figure 2: The four point exchange diagram.
• Figure 3: The four point contact diagram.
• Figure 4: Five point type-a vector diagram.
• Figure 5: Five point type-b vector diagram.