On spinning loop amplitudes in Anti-de Sitter space

TL;DR

This paper develops a systematic momentum space method to compute loop amplitudes for gluons and gravitons in Anti-de Sitter space, extending recent tree-level techniques to loop diagrams.

Contribution

It introduces a differential operator framework to generate loop integrands for AdS Witten diagrams, unifying the computation across different loop topologies.

Findings

Constructed a differential operator for loop integrand generation

Applied the method to bubble, triangle, and box diagrams

Provided a general prescription for loop amplitude calculations

Abstract

In this work we present a systematic study of AdS$_{d+1}$ loop amplitudes for gluons and gravitons using momentum space techniques. Inspired by the recent progress in tree level computation, we construct a differential operator that can act on a scalar factor in order to generate gluon and graviton loop integrands: this systematizes the computation for any given loop level Witten diagram. We then give a general prescription in this formalism, and discuss it for bubble, triangle, and box diagrams.