Abstract
We propose a covariant Hamiltonian action for the Prokushkin and Vasiliev’s matter coupled higher spin gravity in three dimensions. The action is formulated on \( {\mathcal{X}}_4\times {\mathcal{Z}}_2 \) where \( {\mathcal{X}}_4 \) is an open manifold whose boundary contains spacetime and \( {\mathcal{Z}}_2 \) is a noncommutative twistor space. We examine various consistent truncations to models of BF type in \( {\mathcal{X}}_4 \) and \( {\mathcal{Z}}_2 \) with B2 terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value ν ∈ \( \mathrm{\mathbb{R}} \) for the zero-form master field. For ν = 0, we obtain a model on \( {\mathcal{X}}_4 \) containing Blencowe’s action and a model on \( {\mathcal{Z}}_2 \) containing the Prokushkin-Segal-Vasiliev action. For generic ν (including ν = 0), we propose an alternative model on \( {\mathcal{X}}_4 \) with gauge fields in the Weyl algebra of Wigner’s deformed oscillator algebra and Lagrange multipliers in the algebra of operators acting in the Fock representation space of the deformed oscillators.
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ArXiv ePrint: 1512.02209v2
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Bonezzi, R., Boulanger, N., Sezgin, E. et al. An action for matter coupled higher spin gravity in three dimensions. J. High Energ. Phys. 2016, 3 (2016). https://doi.org/10.1007/JHEP05(2016)003
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DOI: https://doi.org/10.1007/JHEP05(2016)003