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Area-preserving diffeomorphisms and higher-spin algebras

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Abstract

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonicd=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphereS 2 as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS 1,1, and can be rewritten as\(\mathop {\lim }\limits_{N \to \infty } su(N,N)\). As an application of our results, we formulate a newd=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms ofS 1,1.

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Authors and Affiliations

  1. Theorey Division, CERN, CH-1211, Geneva 23, Switzerland

    E. Bergshoeff

  2. The Blackett Laboratory, Imperial College, SW7, London, England

    M. P. Blencowe & K. S. Stelle

Authors
  1. E. Bergshoeff
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  2. M. P. Blencowe
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  3. K. S. Stelle
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Communicated by L. Alvarez-Gaumé

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Bergshoeff, E., Blencowe, M.P. & Stelle, K.S. Area-preserving diffeomorphisms and higher-spin algebras. Commun.Math. Phys. 128, 213–230 (1990). https://doi.org/10.1007/BF02108779

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  • DOI: https://doi.org/10.1007/BF02108779

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