Abstract
Bilocal holography is a constructive approach to the higher spin theory holographically dual to O(N ) vector models. In contrast to other approaches to bulk reconstruction, bilocal holography does not take input from the dual gravitational theory. The resulting map is a complete bulk/boundary mapping in that it maps the complete set of O(N ) invariant degrees of freedom in the CFT, to the complete set of higher spin degrees of freedom. After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holography and it gives a robust bulk (entanglement wedge) reconstruction. A gauge invariant entangled pair of CFT degrees of freedom are naturally smeared over a semicircle in the bulk spacetime, which is highly suggestive of bit threads. Finally, we argue that finite N relations in the CFT, when interpreted in the dual AdS spacetime, can provide relations between degrees of freedom located near the boundary and degrees of freedom deep in the bulk.
Highlights
A tower of conserved higher spin currents, each of spin s and dimension ∆ = s + 1
After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holography and it gives a robust bulk reconstruction
How should we think about bit threads? In what follows we argue that bit threads have a natural interpretation within bilocal holography
Summary
We review bilocal holography as developed in [20,21,22,23,24,25,26]. The main novelty in our discussion is a mixed position space/momentum space description, which will be useful when we discuss subregion duality in later sections. The complete set of single trace primaries in the CFT are recovered in the Z → 0 limit from the bulk AdS field Φ(X+, X−, X, Z, θ) This holds at the full quantum level, inside correlation functions, up to contact terms as usual. Using (2.9) and (2.10) to change coordinates, it is a simple application of the chain rule to prove that This is the equation of motion obtained for an arbitrary symmetric higher spin field in light cone gauge in AdS4 [53]. After changing variables to the bilocal field, the subleading terms are generated by an infinite sequence of vertices that arise upon expanding the Jacobian about the leading configuration These interactions should be reproduced by a fully gauge fixed version of Vasilliev’s higher spin theory [16,17,18]. This completes our demonstration that bilocal holography, without any input from the dual higher spin gravity, achieves the correct bulk reconstruction
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