Constructibility of AdS supergluon amplitudes

TL;DR

This paper demonstrates that all tree-level supergluon amplitudes in AdS$_5$ can be systematically constructed using recursive methods based on factorization and flat-space limits, facilitated by a natural R-symmetry basis.

Contribution

It introduces a recursive construction method for AdS supergluon amplitudes leveraging R-symmetry and gauge invariance, providing explicit results up to 8-point amplitudes.

Findings

Recursive construction of amplitudes confirmed up to 8 points.

Simplification achieved through R-symmetry basis and partial amplitudes.

Explicit formulas for scalar and gluon amplitudes included.

Abstract

We prove that all tree-level $n$-point supergluon (scalar) amplitudes in AdS$_5$ can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar color-ordered amplitudes, which reduces the latter to "partial amplitudes" with simpler pole structures and factorization properties. Given the $n$-point scalar amplitude, we first extract spinning amplitudes with $n{-}2$ scalars and one gluon by imposing "gauge invariance", and then use a special "no-gluon kinematics" to determine the $(n{+}1)$-point scalar amplitude completely (which in turn contains the $n$-point single-gluon amplitude). Explicit results of up to 8-point scalar amplitudes and up to 6-point single-gluon amplitudes are included as Supplemental Material.