Light-cone actions and correlators of self-dual theories in AdS$_4$

TL;DR

This paper constructs light-cone actions for self-dual Yang-Mills and Einstein gravity in AdS$_4$, revealing simplified boundary correlators and soft limits that extend flat space results to AdS, highlighting the role of self-dual sectors.

Contribution

It explicitly formulates light-cone actions for self-dual theories in AdS$_4$ and analyzes their boundary correlators and soft limits, connecting self-dual sectors to full theories.

Findings

Boundary correlators are simplified in terms of flat space Feynman diagrams with differential operators.

Soft limits exhibit Weinberg-like factors with derivatives replacing soft poles.

Self-dual sectors are embedded within the full theories via explicit light-cone actions.

Abstract

Self-dual Yang-Mills and Einstein gravity in Euclidean AdS$_4$ are useful toy models because they can be described by simple scalar Lagrangians exhibiting a new manifestation of the colour/kinematics duality, as recently shown by two of the authors. In this paper, we clarify how the self-dual sectors fit into the full theories. In particular, we explicitly construct the light-cone action for Yang-Mills theory and Einstein gravity in AdS$_4$ in terms of positive and negative helicity fields, where we are able to pinpoint the self-dual sector as expected. We then show that the boundary correlators of these theories take a remarkably simple form in terms of Feynman diagrams in half of flat space, acted on by certain differential operators. We also analyse their soft limits and show that they exhibit Weinberg-like soft factors, where the soft pole which appears in scattering amplitudes is replaced by a derivative with respect to the energy.