On big crunch solutions in Prokushkin-Vasiliev theory

Abstract

We construct simple solutions of three-dimensional higher spin gravity interacting with matter in which only the scalar and spin-two fields are excited. They preserve Lorentz symmetry and are similar to the four-dimensional solutions constructed by Sezgin and Sundell, with the difference that the additional twisted sectors of the three-dimensional theory are excited. Furthermore, the three-dimensional system contains an extra parameter $\lambda$ which allows us to vary the mass of the scalar. Among other reasons, the resulting solutions are interesting for the holographic study of cosmological singularities: they describe the growth of a Coleman-De Luccia bubble in anti-de Sitter space, ending in a big crunch singularity. We initiate the holographic study of these solutions, finding evidence for their interpretation within a multi-trace deformation which renders the dual field theory unstable. The limit $\lambda \to 0$ is particularly interesting as it captures effects of a running coupling in a large-$N$ interacting fermion model. We also propose a generalization of our solutions, consisting of a dressing with Lorentz-invariant projectors. This additional sector remains non-trivial when the scalar field is turned off.

Truncation to the 3D minimal bosonic model, clarifications and one reference added. Typos corrected. Version accepted for publication in JHEP

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• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• Planar solutions of higher-spin theory. Nonlinear corrections
• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Action principles for higher and fractional spin gravities
• Higher spin fluctuations on spinless 4D BTZ black hole
• Instantons in AdS${}_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT${}_3$'s
• Higher-spin initial data in twistor space with complex stargenvalues
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity