New relation for AdS amplitudes

TL;DR

The paper develops a momentum-space framework for AdS4 gauge theory amplitudes by decomposing tree-level Witten diagrams into scalar graphs and a projector-based relation between straight and crossed graphs. This yields an algebraic, bulk-integrations-free method to generate higher-point vector amplitudes; straight-line scalar graphs form a basis from which all diagrams can be reconstructed. The approach echoes the flat-space amplitude program and holds potential for revealing deeper AdS amplitude structures and connections to geometric constructs like the amplituhedron, offering a scalable route to rich physical and mathematical insights in holography.

Abstract

In this paper, we present a simple and iterative algorithm that computes Anti-de Sitter space scattering amplitudes. We focus on the vector correlators in AdS in four dimensions in momentum space. These new combinatorial relations will allow one to generate tree level amplitudes algebraically, without having to do any explicit bulk integrations; hence, leading to a simple method of calculating higher point vector amplitudes.

Figures (4)

• Figure 1: A four point Witten diagram
• Figure 2: Decomposition of a five point Witten diagram into scalar graphs
• Figure 3: Algorithm to compute the amplitudes of straight lines
• Figure 4: The six point diagram out of star-triangle topology