Holographic tensor networks from hyperbolic buildings
- URL: http://arxiv.org/abs/2202.01788v2
- Date: Sat, 22 Oct 2022 02:40:45 GMT
- Title: Holographic tensor networks from hyperbolic buildings
- Authors: Elliott Gesteau, Matilde Marcolli and Sarthak Parikh
- Abstract summary: We introduce a unifying framework for the construction of holographic tensor networks.
We give a precise construction of a large family of bulk regions that satisfy complementary recovery.
Our construction recovers HaPPY--like codes in all dimensions, and generalizes the geometry of Bruhat--Tits trees.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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