Non-abelian cubic vertices for higher-spin fields in AdS(d)

Boulanger, Nicolas; Ponomarev, Dmitry; Skvortsov, E. D.

doi:10.1007/JHEP05(2013)008

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Non-abelian cubic vertices for higher-spin fields in AdS(d)

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

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1211.6979
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JHEP2013_05_008.pdf
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Citation

Boulanger, N., Ponomarev, D., & Skvortsov, E. D. (2013). Non-abelian cubic vertices for higher-spin fields in AdS(d). Journal of high energy physics: JHEP, 2013(05): 008. doi:10.1007/JHEP05(2013)008.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-7CB4-F

Abstract

We use the Fradkin-Vasiliev procedure to construct the full set of non-abelian cubic vertices for totally symmetric higher spin gauge fields in anti-de Sitter space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev's simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have nonabelian interactions among themselves and again the number of nonabelian vertices should be given by tensor product multiplicities.