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Title: Holographic tensor networks from hyperbolic buildings
A bstract 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.  more » « less
Award ID(s):
2104330
PAR ID:
10416568
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
10
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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