Flat-space structure of gluon and graviton in AdS

TL;DR

This paper presents a differential representation of gluon and graviton amplitudes in AdS space, revealing flat-space structures and establishing relations like the differential BCJ relation at tree-level.

Contribution

It introduces a novel differential representation for Yang-Mills and gravity amplitudes in AdS, facilitating the understanding of flat-space structures and double copy relations.

Findings

Differential representation of 3- and 4-point amplitudes in AdS.

Revealed flat-space structures using weight-shifting operators.

Established the differential BCJ relation for 4-point Yang-Mills amplitudes.

Abstract

We report the differential representation of three-point and four-point amplitudes for Yang-Mills fields and Einstein gravity in AdS at tree-level. The amplitudes exhibit the flat-space structures by using the weight-shifting operators with reordering, which makes the differential double copy relation at the three-point level straightforward. For four-point Yang-Mills amplitudes, we establish the differential BCJ relation, which can be useful for proving the differential doubly copy at the four-point level in the future.