An action for matter coupled higher spin gravity in three dimensions

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 $$ {mathcal{x}}_4times {mathcal{z}}_2 $$ 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.