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Characteristic cohomology and observables in higher spin gravity. (English) Zbl 1457.83054

Summary: 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.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83E05 Geometrodynamics and the holographic principle
81T11 Higher spin theories
58J28 Eta-invariants, Chern-Simons invariants
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