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Matter-free higher spin gravities in 3D: Partially-massless fields and general structure

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

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

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2005.05931.pdf
(Preprint), 508KB

PhysRevD.102.066003.pdf
(Publisher version), 535KB

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Citation

Grigoriev, M., Mkrtchyan, K., & Skvortsov, E. (2020). Matter-free higher spin gravities in 3D: Partially-massless fields and general structure. Physical Review D, 102: 066003. doi:10.1103/PhysRevD.102.066003.


Cite as: http://hdl.handle.net/21.11116/0000-0006-84CA-1
Abstract
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a form of the flatness condition for a connection of a Lie algebra, which, provided there is a non-degenerate invariant bilinear form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the frame-like formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent formulation approach, we also obtain an explicit uplift of any given metric-like vertex to its frame-like counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metric-like vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices.