Supergluon scattering in AdS: constructibility, spinning amplitudes, and new structures

TL;DR

This paper develops a recursive method to compute supergluon and spinning amplitudes in AdS space, revealing new structural insights and providing explicit formulas up to seven points, advancing the understanding of AdS scattering processes.

Contribution

It introduces an improved proof of constructibility for supergluon and spinning amplitudes in AdS, and derives simple Feynman rules and hidden structural properties for these amplitudes.

Findings

Explicit formulas for up to 7-point supergluon amplitudes

Identification of pole structures and truncation on descendent poles

Universal behavior analogous to flat-space soft/collinear limits

Abstract

We elaborate on a new recursive method proposed in arXiv:2312.15484 for computing tree-level $n$-point supergluon amplitudes as well as those with one gluon, i.e., spinning amplitudes, in ${\rm AdS}_5 \times S^3$. We present an improved proof for the so-called "constructibility" of supergluon and spinning amplitudes based on their factorizations and flat-space limit, which allows us to determine these amplitudes in Mellin space to all $n$. We present explicit and remarkably simple expressions for up to $n=7$ supergluon amplitudes and $n=6$ spinning amplitudes, which can be viewed as AdS generalizations of the scalar-scaffolded gluon amplitudes proposed recently. We then reveal a series of hidden structures of these AdS amplitudes including (1) an understanding of general pole structures especially the precise truncation on descendent poles (2) a derivation of simple "Feynman rules" for the all-$n$ amplitudes with the simplest R-symmetry structures, and (3) certain universal behavior analogous to the soft/collinear limit of flat-space amplitudes.