Higher spin dynamics in gravity and w1+∞ celestial symmetries

In this paper we extract from a large-r 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 w1+infinity loop algebra on the gravitational phase space.

Automated summary

In this paper, we extract a dynamical system describing the time evolution of an infinity of higher-spin charges from the large-r expansion of the vacuum Einstein's equations. We evaluate the canonical action of these charges on the gravity phase space through integration. Truncating this action to quadratic order and considering the associated charge conservation laws, we obtain an infinite tower of soft theorems. We demonstrate that the canonical action of the higher spin charges on gravitons and the conformally soft gravitons in a conformal primary basis reproduce the higher spin celestial symmetries derived from the operator product expansion. Additionally, we provide direct evidence that these charges form a canonical representation of a w1+infinity loop algebra on the gravitational phase space.