Abstract
We present exact solutions to Vasiliev’s bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in space-time, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (A)dS4. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.
Highlights
Vasiliev’s theory in four dimensions [1] has so far been studied mainly around its maximally symmetric anti-de Sitter vacuum
We present exact solutions to Vasiliev’s bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds
We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description
Summary
Vasiliev’s theory in four dimensions [1] has so far been studied mainly around its maximally symmetric anti-de Sitter vacuum. While we shall leave to a future work an analysis of the the holographic aspects of the exact solutions that we present here, we propose to interpret the domain walls as bulk duals of vacua of three-dimensional massive quantum field theories arising through spontaneous breaking of conformal (higher spin) symmetries; for a relatively recent study of spontaneous breaking of scale invariance in certain CFTs in D = 3, see [16]. One needs to distinguish between singularities that are gauge artifacts and genuine singularities in the full (x, Y, Z) space, sometimes referred to as the correspondence space Details of the passage to Vasiliev gauge in leading order are given in appendix D, and useful formula in the description of twistor space distributions and the star products of relevant projector operators are provided in appendix E
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