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Journal Article

Characteristic Cohomology and Observables in Higher Spin Gravity


Skvortsov,  Evgeny
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Sharapov, A., & Skvortsov, E. (2020). Characteristic Cohomology and Observables in Higher Spin Gravity. Journal of High Energy Physics, 2020(12): 190. doi:10.1007/JHEP12(2020)190.

Cite as: http://hdl.handle.net/21.11116/0000-0006-C138-1
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.