Simplicity in AdS Perturbative Dynamics

TL;DR

This paper explores the analytic structure of loop-level perturbative dynamics in pure AdS space, revealing unexpected simplicity in pole structures and proposing conjectures for all-loop diagrams based on explicit two-loop evidence.

Contribution

It introduces a new recursive construction for Mellin amplitudes in AdS, proposes conjectures for all-loop diagrams, and develops alternative diagrammatic rules and contour analysis methods.

Findings

Simplified pole structure in Mellin amplitudes and pre-amplitudes.

Evidence supporting conjectures for all-loop diagram structures.

New diagrammatic rules and improved contour analysis techniques.

Abstract

We investigate analytic properties of loop-level perturbative dynamics in pure AdS, with the scalar effective theories with non-derivative couplings as a prototype. Explicit computations reveal certain (perhaps unexpected) simplicity regarding the pole structure of the results, in both the Mellin amplitude and a closely related object that we call Mellin pre-amplitude. Correspondingly we propose a pair of conjectures for arbitrary diagrams at all loops, based on non-trivial evidence up to two loops (and higher loops in a special class of diagrams). We also inspect the structure of residues at poles in the physical channels for several one-loop examples up to a 4-point box, as well as a two-loop double-triangle diagram. These analyses are performed using the recursive construction of Mellin (pre-)amplitudes recently prescribed in arXiv:1710.01361, for which we provide detailed derivation and generalization in this paper. Along the way we derive a set of alternative diagrammatic rules for tree (pre-)amplitudes, which are better suited to our loop construction. On the mathematical aspect we share some new thoughts on improving the contour analysis of multi-dimensional Mellin integrals, which are the essential ingredients that make our approach practical.