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arXiv · 2202.01788

Holographic tensor networks from hyperbolic buildings

Elliott Gesteau·Matilde Marcolli·Sarthak Parikh
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Abstract

We introduce a unifying framework for the construction of holographic tensor networks, based on the theory of hyperbolic buildings. The underlying dualities relate a bulk space to a boundary which can be homeomorphic to a sphere, but also to more general spaces like a Menger sponge type fractal. In this general setting, we give a precise construction of a large family of bulk regions that satisfy complementary recovery. For these regions, our networks obey a Ryu--Takayanagi formula. The areas of Ryu--Takayanagi surfaces are controlled by the Hausdorff dimension of the boundary, and consistently generalize the behavior of holographic entanglement entropy in integer dimensions to the non-integer case. Our construction recovers HaPPY--like codes in all dimensions, and generalizes the geometry of Bruhat--Tits trees. It also provides examples of infinite-dimensional nets of holographic conditional expectations, and opens a path towards the study of conformal field theory and holography on fractal spaces.

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BibTeXRIS

Elliott Gesteau, Matilde Marcolli, Sarthak Parikh. 2022-10-22. Holographic tensor networks from hyperbolic buildings. https://doi.org/10.1007/jhep10(2022)169

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