Abstract
Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin Weyl tensors are found in a closed form and are shown to have the double copy origin. The effect of higher-spin fields to form a strictly positive scalar condensate for any values of higher-spin charges is observed.
Highlights
Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions
A particular attention is paid to the linearized pure s = 2 case corresponding to the standard GR black brane
We would like to analyze HS equations that follow from the generating system in perturbations rather than the Vasiliev system itself in this paper as this gives us control over locality of HS interactions at lowest orders which otherwise is hard to trace back
Summary
HS interactions (1.1), (1.2) can be extracted from the Vasiliev generating system [6]. Free propagation of HS fields around AdS vacuum (2.5) is described by the gauge invariant twisted-adjoint covariant constancy condition on the 0-form C(y, y; k, k|x) and by the on-mass-shell condition in the sector of gauge fields parameterized by 1-form w(y, y; k, k|x). Bosonic embedding There is a well known truncation of the supersymmetric theory that leads to the bosonic HS model having each field appearing once. It is governed by certain automorphism of the full Vasiliev equations, which allows one to set. While the bosonic embedding is defined at the level of full equations of motion, there is yet another embedding capturing each spin s field only once that can be defined at least perturbatively in four dimensions.
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