Characteristic Cohomology and Observables in Higher Spin Gravity

TL;DR

This paper classifies dynamical invariants in higher spin gravity models across dimensions, revealing numerous conserved currents and suggesting hidden integrability, based on advanced cohomological computations.

Contribution

It provides a complete classification of invariants in higher spin gravity, including new insights into conserved currents and a novel invariant in Chern-Simons theory.

Findings

Many conserved p-form currents found, indicating hidden integrability.

Complete classification of invariants in 3d and 4d higher spin models.

Introduction of a new invariant in Chern-Simons theory with Weyl algebra.

Abstract

We give a complete classification of dynamical invariants in $3d$ and $4d$ Higher Spin Gravity models, with some comments on arbitrary $d$. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved $p$-form currents with various $p$. The last fact, being in tension with `no nontrivial conserved currents in quantum gravity' and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley--Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.