An Action for Matter Coupled Higher Spin Gravity in Three Dimensions

Roberto Bonezzi; Nicolas Boulanger; Ergin Sezgin; Per Sundell

doi:10.1007/JHEP05(2016)003

paper

An Action for Matter Coupled Higher Spin Gravity in Three Dimensions

arXiv:1512.02209 · doi:10.1007/JHEP05(2016)003

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 $X_{4} \times Z_{2}$ where $X_{4}$ is an open manifold whose boundary contains spacetime and $Z_{2}$ is a noncommutative twistor space. We examine various consistent truncations to models of BF type in $X_{4}$ and $Z_{2}$ with B $^{2}$ terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value $ν \in R$ for the zero-form master field. For $ν = 0$ , we obtain a model on $X_{4}$ containing Blencowe's action and a model on $Z_{2}$ containing the Prokushkin--Segal--Vasiliev action. For generic $ν$ (including $ν = 0$ ), we propose an alternative model on $X_{4}$ 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.

33 + 1 pages, no figure. Minor typos corrected

An Action for Matter Coupled Higher Spin Gravity in Three Dimensions

Abstract

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