Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries
Abstract
In this paper we extract from a large- expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion. Finally, we give direct evidence that these charges form a canonical representation of a loop algebra on the gravitational phase space.
Keywords
Cite
@article{arxiv.2112.15573,
title = {Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries},
author = {Laurent Freidel and Daniele Pranzetti and Ana-Maria Raclariu},
journal= {arXiv preprint arXiv:2112.15573},
year = {2022}
}
Comments
30 pages + appendices; v2 Added a section on the exact match between the linearized Einstein's equations and the charge recursion relation. Included details on the relation between the tower of sub-leading components of the $\Psi_0$ Weyl scalar, the Newman-Penrose charges and the higher-spin charges and identified these Weyl scalar components in the associated celestial diamonds