Communications in Mathematical Physics

, Volume 128, Issue 2, pp 213–230 | Cite as

Area-preserving diffeomorphisms and higher-spin algebras

  • E. Bergshoeff
  • M. P. Blencowe
  • K. S. Stelle


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-sphereS2 as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS1,1, 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 ofS1,1.


Neural Network Statistical Physic Field Theory Complex System Gauge Theory 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • E. Bergshoeff
    • 1
  • M. P. Blencowe
    • 2
  • K. S. Stelle
    • 2
  1. 1.Theorey DivisionCERNGeneva 23Switzerland
  2. 2.The Blackett LaboratoryImperial CollegeLondonEngland

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