A stereoscopic look into the bulk

By B. Czech, L. Lamprou, Sam McCandlish, B. Mosk, J. Sully. 2016

249 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6efe612af357f0e903d130eeb0181da587474499

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Citations in the corpus

Solving the Schwarzian via the conformal bootstrap (2017, methodology): “In the past few years it has been recognized that holographic CFTs at finite temperature exhibit characteristics of many body quantum chaos [1, 2, 3, 4, 5].”
Holographic symmetry algebras for gauge theory and gravity (2021, background): “conformal blocks (see OPE blocks from [68], reviewed in App.”
Geometry of Krylov complexity (2021, background): “In this setup, the OPE does not collapse to a single operator but is expanded in terms of OPE blocks, see [65, 97, 98].”
Averaged null energy condition from causality (2016, background): “(4)See [42] for recent progress in writing general OPEs by integrating over causal diamonds.”
Remarks on the Sachdev-Ye-Kitaev model (2016, methodology): “This is a general feature of the Casimir operator acting on bilocal fields as has been used recently in [30].”
Light-ray operators in conformal field theory (2018, background): “mes from regions of the integral where the OPE is not valid inside the integrand. By contrast, there is a simple integral representation for a block alone (without its shadow) in Lorentzian signature [110]. The reason is that in Lorentzian signature, we can integrate over a conformally-invariant reg”
A general proof of the quantum null energy condition (2017, background): “ion for the stress tensor OPE block of two auxiliary time like separated scalars, which turns out to be just the half modular Hamiltonian operator for the double cone region between the two operators [90,91]. This region can be conformally mapped to the Rindler wedge. Thus the rst term is just the s”
Weight shifting operators and conformal blocks (2017, unknown): “One can alternatively isolate the conformal block by performing the integral in Lorentzian signature over a domain defined by the lightcones of the four points x1, x2, x3, x4 [139].”
TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, methodology): “For one thing, the twopoint function of a scalar field in AdS is ultimately determined by conformal invariance, so in fact the bulk scalar field we reconstructed in the previous section could have been reconstructed just as well in any boundary conformal field theory, even one without a semiclassica”
Comments on holographic complexity (2016, background): “It might also be interesting to extend the holographic complexity calculations to connect to the constructions appearing in [58, 59, 60, 61], where other fields are integrated over surfaces and regions in the bulk.”
Bulk locality from modular flow (2017, background): “When the modular hamiltonian is local, such as for a spherical region in a CFT, this expression generalizes the OPE block story of [28, 29, 30].”