Holography of the Script N = 1 higher-spin theory on AdS₄

Abstract

We argue that the N = 1 higher-spin theory on AdS 4 is holographically dual to the N = 1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.

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

“…Being based on the parity automorphism of the nonlinear HS theory, the A condition at η =η and B condition at η = −η can be imposed in all orders of the perturbative expansion. This conclusion matches the wellknown fact [23,68,74] that the A-model with A boundary conditions and B-model with B conditions correspond to free conformal bosons and fermions on the boundary (see also [30] and references therein). For any other boundary conditions and/or phases of η the boundary dual theory is not free.…”

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

“…In a specific gauge, certain linearized perturbations of the noncommutative twistor space structure give rise to Fronsdal fields. 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.…”

“…As we shall see, the real-analyticity requirement constrains the initial data in the Weyl zero-form already at the linearized level. 7 More specifically, the new sector of the fiber algebra is isomorphic to the group algebra C[Z × Z] where Z × Z is generated by two elements in Sp(4; C) given by exponentials of a pair of Cartan generators of sp(4; R). These correspond to linear symmetries of the two-dimensional harmonic oscillator, and generate the Killing symmetries of the solutions (including higher spin symmetries).…”

“…6 Whether a more general vacuum gauge function can introduce additional classical moduli remains an open problem. 7 An optional criterion is that the fiber algebra is a unitarizable representation of the higher spin algebra and hence the anti-de Sitter isometry algebra; we expect this property to arise at higher orders of classical perturbation theory by requiring positivity of a suitable free energy functional. 8 For recent reformulations containing the original Vasiliev system as consistent truncations, see [24,38].…”

A Note on Rectangular Partially Massless Fields

“…This can be seen for instance from the decomposition of the tensor product of two spin-s singletons spelled out in [10], where one can check that there are no currents of spin lower than 2s. 5 Notice that by changing the boundary condition of fields in the bulk opens the possibility of having an HS theory dual to an interacting CFT, see for instance [22,25,28,49,50]. From the CFT point of view, this corresponds to the modification of the previously mentioned Maldacena-Zhiboedov theorem studied by the same authors in [51].…”