Construction of bulk fields with gauge redundancy

199

495

We present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural CFT operators whose duals are simple, diffeomorphisminvariant bulk operators. The CFT operators of interest are the "OPE blocks," contributions to the OPE from a single conformal family. In holographic theories, we show that the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. One widely studied example of an OPE block is the modular Hamiltonian, which is dual to the fluctuation in the area of a minimal surface. Thus, our operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields.Although the OPE blocks are non-local operators in the CFT, they admit a simple geometric description as fields in kinematic space -the space of pairs of CFT points. We develop the tools for constructing local bulk operators in terms of these non-local objects. The OPE blocks also allow for conceptually clean and technically simple derivations of many results known in the literature, including linearized Einstein's equations and the relation between conformal blocks and geodesic Witten diagrams.

Section: Jhep07(2016)129 4 Construction Of Bulk Local Operatorsmentioning

confidence: 84%

A stereoscopic look into the bulk

Czech

Lamprou

McCandlish

et al. 2016

199

495

“…Following [43,44], we do this by choosing a cutoff surface at large but finite radius, with induced metric S d−1 × R, and then specifying bulk points by sending in spacelike geodesics from the t = 0 slice of this cutoff surface that start out orthogonal to the S d−1 directions. We then take the limit as the cutoff surface approaches the boundary.…”

Section: Defining Local Operatorsmentioning

confidence: 99%

Bulk locality and quantum error correction in AdS/CFT

Almheiri

Dong

Harlow

2015

704

1,132

We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

“…Any such construction will at best be perturbative in the gravitational coupling constant, which I will refer to as 1/N . For small numbers of operators any backreaction can be treated perturbatively, so by an appropriate gauge fixing [32,33] we can treat the bulk theory as a quantum field theory in curved spacetime (the gravitons will JHEP11(2014)055 just be another matter field). It will be an effective field theory with nontrivial irrelevant operators appearing that are suppressed by powers of 1/N ; their coefficients can in principle be determined by comparison with the CFT.…”

Section: The Basics Of Reconstructionmentioning

confidence: 99%

“…But if I don't know you are going to do this, then my O operators are automatically redefined in such a way that I see a smooth horizon when I jump in, even though the quantum state of the black hole is the same in either case. The full state of 32 These are the types of equilibrium states one would construct acting on |ψ with the "unitary behind the horizon" type operators discussed in section 3, but here I will follow the rules of PR and construct mirror operators which see the "horizon" as unexcited.…”

Section: Including the Infalling Observermentioning

confidence: 99%

See 1 more Smart Citation

Aspects of the Papadodimas-Raju proposal for the black hole interior

Harlow

2014

116

In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1/N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the "state-dependence" of the proposal with more familiar phenomena, arguing that, unlike in quantum mechanics, the measurement process (including the apparatus) in something like the PR proposal or its earlier manifestations cannot be described by unitary evolution. These issues render the proposal somewhat ambiguous, and it seems new ideas would be needed to make some version of it work. I close with some brief speculation on to what extent quantum mechanics should hold for the experience of an infalling observer.