Abstract
We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality.
Highlights
By the corresponding collective action. It was proposed and in subsequent studies established that the bi-local space contains precisely the sufficient degrees of freedom to allow a representation of bulk fields and their dynamics in AdS space-time [1,2,3,4]
We have in this paper developed the details of the covariant bi-local holographic reconstruction of bulk AdS applicable to cases of vectorial AdS duality
Different theories are distinguished by different bi-local propagators, while the all order interaction vertices are universally specified by the collective field action
Summary
Bi-local holography provides a scheme of constructing various higher spin type bulk AdS theories from large N vector type CFT’s. It is based on the collective field approach to the 1/N expansion where one exactly represents the path integral. For the Euclidean d-dimensional conformal field theory, the two Casimir operators of the SO(1, d + 1) conformal symmetry, whose generators are denoted by LAB (A, B = −1, 0, · · · , d), are defined by The eigenvalues of these operators acting on a primary with conformal dimension ∆ and spin s are given in [26].2.
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