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Geometry as Compression

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There appear to be deep connections between geometry and entropy. This connection was first seen in black hole thermodynamics, but has been more fully realized in the Ryu-Takayanagi procedure for calculating entanglement entropies in AdS/CFT. We suggest that this connection is even broader: entropy, and in particular compression, are the fundamental building blocks of emergent geometry. We demonstrate how spatial geometry can be derived from the properties of a recursive compression algorithm for the boundary CFT . We propose a general algorithm for constructing MERA -like tensor networks and elucidate connections to the mathematical field of integral geometry. We arrive at a new, non-perturbative refinement of the spacetime entanglement conjecture.

This talk is part of the DAMTP Friday GR Seminar series.

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