An action for matter coupled higher spin gravity in three dimensions

DOI10.1007/JHEP05(2016)003zbMATH Open1388.83566arXiv1512.02209MaRDI QIDQ1638617

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Publication date: 12 June 2018

Published in: (Search for Journal in Brave)

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 ${calX}_{4}imes{calZ}_2$ where ${calX}_4$ is an open manifold whose boundary contains spacetime and ${calZ}_2$ is a noncommutative twistor space. We examine various consistent truncations to models of BF type in ${calX}_4$ and ${calZ}_2$ with B${}^2$ terms and central elements. They are obtained by integrating out the matter fields in the presence of a vacuum expectation value $uinmathbbR$ for the zero-form master field. For $u=0$, we obtain a model on ${calX}_4$ containing Blencowe's action and a model on ${calZ}_2$ containing the Prokushkin--Segal--Vasiliev action. For generic $u$ (including $u=0$), we propose an alternative model on ${calX}_4$ 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.

Full work available at URL: https://arxiv.org/abs/1512.02209

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