An Exact Solution of 4D Higher-Spin Gauge Theory

TL;DR

The paper delivers the first exact, non-AdS background in four-dimensional higher-spin gauge theory by solving the Vasiliev master-field equations with an $SO(3,1)$-invariant ansatz. It shows that all higher-spin fields vanish and the metric remains Weyl-flat, while the solution connects two asymptotically $AdS_4$ regions through $dS_3$-foliated domain walls and $H_3$-foliated FRW-like patches, controlled by a real zero-form parameter $ u$. The authors develop and compare multiple solution-generation techniques, including a $Z$-space gauge-function method, perturbative spacetime embedding, and analysis of initial data regularity, plus zero-form curvature invariants that classify solutions. They further explore non-maximally symmetric sectors, domain-wall and RW-like truncations, and provide integral-analytic constructions of symmetry parameters to second order. The work advances the understanding of exact HS solutions, offers a framework for holographic interpretation, and motivates further study of higher-spin geometry in cosmological-like settings.

Abstract

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker spacetimes -- one in the future and one in the past -- with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants.