Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity

TL;DR

This paper develops an extended phase space framework at null infinity for self-dual Yang-Mills and gravity theories, revealing the symmetry structure of their infrared behavior and establishing a novel double copy relation at all orders.

Contribution

It introduces a systematic construction of phase space extensions at all orders in r for self-dual theories and derives a new double copy mapping for gauge transformations and diffeomorphisms.

Findings

Extended phase space formalism at null infinity for all orders in r.

A new double copy relation between YM gauge transformations and gravity diffeomorphisms.

Formalization of the symmetry origin of infrared behavior in self-dual theories.

Abstract

Working in the self-dual sector for Yang-Mills and gravity, we show how to construct an extended phase space at null infinity, to all orders in the radial expansion. This formalises the symmetry origin of the infrared behaviour of these theories to all sub-leading orders. As a corollary, we also derive a double copy mapping from a subset of YM gauge transformations to a subset of diffeomorphisms to all orders in the transformation parameters, which to our knowledge has not been presented before in the literature.