Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity

TL;DR

This paper constructs a non-perturbative realization of higher spin symmetries in gravity, introducing a symmetry algebroid that includes radiation effects and preserves Noether charges asymptotically.

Contribution

It develops a non-perturbative algebraic framework for higher spin symmetries in gravity, extending previous algebraic structures to include radiation and asymptotic phase space.

Findings

Defined a symmetry algebroid $\

Realized a non-linear, non-perturbative Noether charge on the asymptotic phase space.

Showed the algebroid reduces to the wedge symmetry algebra in non-radiative cases.

Abstract

In this paper we construct a non-perturbative action of the higher spin symmetry algebra on the gravitational phase space. We introduce a symmetry algebroid $\mathcal{T}$ which allows us to include radiation in an algebraic framework. We show that $\mathcal{T}$ admits a non-linear realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. Besides, this Noether charge is conserved in the absence of radiation. Moreover, at non radiative cuts, the algebroid can be restricted to the wedge symmetry algebra studied in ArXiv:2409.12178. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Einstein's equations. This result then guarantees that the underlying symmetry algebra is also represented canonically.