Current interactions and holography from the 0-form sector of nonlinear higher-spin equations

Abstract

The form of higher-spin current interactions in AdS 4 is derived from the full nonlinear higher-spin equations in the sector of Weyl 0-forms. The coupling constant in front of spin-one currents built from scalars and spinors as well as Yukawa coupling are determined explicitly. Couplings of all other higher-spin current interactions are determined implicitly. All couplings are shown to be independent of the phase parameter of the nonlinear higher-spin theory. The proper holographic dependence of the vertex on the higher-spin phase parameter is shown to result from the boundary conditions on the bulk fields.

4D higher spin black holes with nonlinear scalar fluctuations

“…The former path, whereby the internal degrees of freedom of Vasiliev's integrable system are viewed essentially as auxiliary fields, without any proper dynamics of their own, involves a reduction down to a set of deformed Fronsdal equations on the spacetime submanifold [4, 7-9, 13, 30, 84, 92-95], to be directly compared with those of the quasi-local deforrmed Fronsdal theory. Although this procedure introduces ambiguities concerning the embedding of spacetime into the full noncommutative geometry and the internal gauge fixing, one may entertain the idea that the quasi-locality requirement provides a guiding principle; for recent progress, see [95][96][97].…”

New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity

“…The GKPW prescription applies to the quasilocal theory by construction, as its action has self-adjoint kinetic terms, and the resulting holographic correlation functions indeed correspond to free three-dimensional conformal field theories. 2 Recent work [22] shows that there exists an explicit field redefinition that maps Vasiliev's theory to a quasi-local theory on-shell, obtained by carefully fine-tuning the perturbative expansion on the Vasiliev side, though it remains to be seen whether it coincides with that of [18]. Moreover, as later shown in [23] the required field redefinition is large, and hence it is unclear to what extent the method can be used to actually compute any holographic correlation functions.…”

“…In other words, an asymptotic observer who sources the bulk using a linearized spin-s Fronsdal field will activate the corresponding component field given above, whose boundary value can thus be identified with a dual conformal field theory source coupled to a conserved spin-s current. The higher order couplings depend on the choice of gauge as well as the initial data for Φ and W µ ; as proposed by Vasiliev [22], these initial data can be fine-tuned at higher orders in order to obtain quasi-local equations of motion in the gauge (2.60).…”

“…The expression H 2 F αβ − HαβG αα G ββ can be factorized as Then, assuming that ν 1,0,0 = 0 = ν 2,0,0 , (4.20) 22 We note the useful relations F 2 := 1 2 F αβ (F) αβ = det (F) and F αβ F βγ = F 2 δα γ , idem H.…”

A Note on Rectangular Partially Massless Fields

“…2 See e.g., [6] where those properties were studied using the harmonic expansion of fields in (A)dS spacetimes. of all cubic vertices and the quartic vertex for four scalar fields in the bulk [36,37], as dictated by the holographic duality, while [38] also raising questions on the locality properties of the bulk HS theory (see e.g., [39][40][41][42][43] and references therein for more details).…”