Higher Spins in AdS and Twistorial Holography

On nonlinear higher spin curvature

“…Applying (4.10) and (4.12) we can rewrite the latter variation in the following way: To compare the results of this paper to the ones obtained in AdS space by Vasiliev and collaborators (see [5] and references therein), one should continue this results from flat space to the AdS as it was done for linear curvatures in [24,25]. The AdS continuation of the obtained second order curvature is relevant also to AdS/CFT tasks (see [23], [26], [27], [28]), and we hope to be able to do it in near future.…”

Perturbations of $ \mathcal{W} $ ∞ CFTs

“…It relates a Vasiliev higher spin theory [7] on AdS 4 to the large N limit of the O(N ) vector model in 3 dimensions. Compelling evidence for this duality was recently found by comparing correlation functions in [8,9], as well as through the work [10,11] that determined interesting general constraints on the structure of the correlation functions based on symmetry considerations. More recently, these dualities were further generalised to a one-parameter family of (in general) parity-breaking theories in [12,13,14].…”

“…) where B + is a shorthand for B(Λ + ), and similarly for the others. 9 Therefore for the state (Λ + ; Λ − ) to have conformal dimension 1+λ 2 in the 't Hooft limit we need…”

Differential Poisson Sigma Models with Extended Supersymmetry

“…Compared to earlier holography proposals [19,20,21], in which the bulk side is a (string) field theory containing higher spin gravity of Vasiliev type [22,23], the proposal of [17] was based on the observation that tensionless strings in anti-de Sitter spacetime behave as collections of conformal particles, that is, on a first-quantized description of the bulk physics. Subsequent tests at the level of on-shell amplitudes in AdS 4 , have shown that traces of Gaussian density matrices of the the quantum mechanical harmonic oscillator in two dimensions describing unfolded boundary-tobulk propagators of massless fields [24], which one may think of as vertex operators on conformal particle worldlines in phase space 4 , or, boundary vertex operators on the corresponding topological open string, indeed reproduce the correlation functions for bilinear operators in free conformal field theories in three dimensions [25,26,27,28] 5 . The current, slightly refined, working hypothesis is that there exists a variant of Witten's realization of Chern-Simons theory as a topological A model [29] (see also [30]), whereby a gauging of the differential Poisson sigma model with 3-graded Chan-Paton factors [31] (see also [32,33]) yields the Frobenius-Chern-Simons formulation [34,35] of higher spin gravity.…”