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Register a new userTowards higher-spin holography in ambient space of any dimension
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We derive the propagators for higher-spin master fields in anti-de Sitter space of arbitrary dimension. A method is developed to construct the propagators directly without solving any differential equations. The use of the ambient space, where AdS is represented as a hyperboloid and its conformal boundary as a projective light-cone, simplifies the approach and makes a direct contact between boundary-to-bulk propagators and two-point functions of conserved currents.
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We aim at formulating a higher-spin gravity theory around AdS$_2$ relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by $hs[lambda]$ and parameterized by a real parameter $lambda$. The singleton is defined to be a Verma module of the AdS$_2$ isometry subalgebra $so(2,1) subset hs[lambda]$ with conformal weight $Delta = frac{1pmlambda}{2},$. On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS$_2$ with ascending masses expressed in terms of $lambda$. On the other hand, the higher-spin fields arising through the gauging of $hs[lambda]$ algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS$_2$ higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT$_1$ duals of the kinematical structures identified in the bulk.
We derive the spectrum of gauge invariant operators for maximally supersymmetric Yang-Mills theories in d dimensions. After subtracting the tower of BPS multiplets, states are shown to fall into long multiplets of a hidden SO(10,2) symmetry dressed by thirty-two supercharges. Their primaries organize into a universal, i.e. d-independent pattern. The results are in perfect agreement with those following from (naive) KK reduction of type II strings on the warped AdS x S near-horizon geometry of Dp-branes.
A minimal requirement for any strongly coupled gauge field theory to have a classical dual bulk gravity description is that one should in principle be able to recover the full geometry as encoded on the asymptotics of the spacetime. Even this requirement cannot be fulfilled with arbitrary precision simply due to the fact that the boundary data is inherently noisy. We present a statistical approach to bulk reconstruction from entanglement entropy measurements, which handles the presence of noise in a natural way. Our approach therefore opens up a novel gateway for precision holography.
We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by G{u}rdogan and one of the authors as a strong-twist double scaling limit of $gamma$-deformed $mathcal{N}=4$ SYM theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by fishnet Feynman graphs and is integrable in the planar limit. The dynamics of these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain. In $2D$ it is the analogue of L. Lipatovs $SL(2,mathbb{C})$ spin chain for the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$. Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the authors to any $D$ we compute exactly, at any coupling, a four point correlation function, dominated by the simplest fishnet graphs of cylindric topology, and extract from it exact dimensions of R-charge 2 operators with any spin and some of their OPE structure constants.
The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory.
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