Bulk curves from boundary data in holography
By Vijay Balasubramanian, Borun D. Chowdhury, B. Czech, J. Boer, M. Heller. 2013
193 citations recorded by the source corpus.
We embed spherical Rindler space—a geometry with a spherical hole in its center—in asymptotically anti– de Sitter (AdS) spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is holographically dual to an ultraviolet sector of the boundary field theory given by restriction to a strip of finite duration in time. Because measurements have finite durations, local observers in the field theory can only access information about bounded spatial regions. We propose a notion of differential entropy that captures uncertainty about the state of a system left by the collection of local, finite-time observables. For two-dimensional conformal field theories we use holography and the strong subadditivity of entanglement to propose a formula for differential entropy and show that it precisely reproduces the areas of circular holes in AdS 3 . Extending the notion to field theories on strips with variable durations in time, we show more generally that differential entropy computes the areas of all closed, inhomogeneous curves on a spatial slice of AdS 3 . We discuss the extension to higher-dimensional field theories, the relation of differential entropy to entanglement between scales, and some implications for the emergence of space from the renormalization group flow of entangled field theories.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c59ed0e94f364d996445f519b489968a2243dc19
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Citations in the corpus
- A stereoscopic look into the bulk (2016, methodology): “dence. Its implications, however, are more consequential. Recall that kinematic space and integral geometry emerged as essential tools for reconstructing the bulk geometry from entanglement entropies [9,47]. With our operator correspondence at hand, we were able to use closely related machinery to a”
- On the architecture of spacetime geometry (2012, background): “Finally, recently boundary observables have been found which yield the Bekenstein–Hawking entropy (2) of arbitrary surfaces in the bulk spacetime [13]”