Higher spins in AdS and twistorial holography

Abstract

In this paper we simplify and extend previous work on three-point functions in Vasiliev's higher spin gauge theory in AdS 4 . We work in a gauge in which the space-time dependence of Vasiliev's master fields is gauged away completely, leaving only the internal twistor-like variables. The correlation functions of boundary operators can be easily computed in this gauge. We find complete agreement of the tree level three point functions of higher spin currents in Vasiliev's theory with the conjectured dual free O(N ) vector theory.

One-loop effective actions and higher spins. Part II

“…Other papers of ours, related to the present one are, beside [1,42,43]. For future developments we think that important references are [44][45][46][47].…”

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

“…This suggests a holographic relationship to three-dimensional conformal field theories [3][4][5]; see also [6][7][8]. In [9,10] this relation was examined under the assumption that the Gubser-Klebanov-Polyakov-Witten (GKPW) prescription [11,12] for on-shell computations of Witten diagrams can be applied to classical field configurations obtained from Vasiliev's equations. However, the Fronsdal fields embedded into Vasiliev's master fields have non-local interactions [13][14][15] 1 that belong to a functional class widely separated [17] from that of the quasi-local Fronsdal theory [18], which is built by applying the canonical Noether approach to Fronsdal fields in anti-de Sitter spacetime.…”

“…9 Taking the master fields to be smooth functions of Y4 yields an anti-de Sitter analog of the PenroseNewman transformation; to our best understanding, the precise relation between Y4 × Z4 and the original (commuting) twistor space of Penrose remains to be spelled out in detail. 10 The doublet indices are raised and lowered using f α = ε αβ f β and f β = f α ε αβ idem fα.…”

“…Beyond the linearized approximation, it has been used in amplitude computations [9,10,28,29] and related recent works [38,40]. Most exact solutions found so far, however, have been given in other gauges argued to be equivalent to Vasiliev gauge; for example, see [26,37,41].…”

“…where e αα µ = − λδ a µ (σ a ) αα h 2 , (C.9) 10) are the vierbein and Lorentz connection of AdS 4 in stereographic coordinates, with flat indices converted to spinor ones using van der Waerden symbols. One also has…”