Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 038, 18 pages      arXiv:0907.3195

Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

Xavier Bekaert a and Maxim Grigoriev b
a) Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 6083 du CNRS, Fédération Denis Poisson, Université Francois Rabelais, Parc de Grandmont, 37200 Tours, France
b) Tamm Theory Department, Lebedev Physics Institute, Leninsky prospect 53, 119991 Moscow, Russia

Received November 09, 2009, in final form April 23, 2010; Published online May 07, 2010

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.

Key words: higher symmetries; conformal symmetry.

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