Tensor network and ($p$-adic) AdS/CFT

Abstract

We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed $p$-adic AdS/CFT correspondence (a holographic duality based on the $p$-adic number field ${\mathbb{Q}}_p$). Instead of assuming the $p$-adic AdS/CFT correspondence, we show how important features of AdS/CFT such as the bulk operator reconstruction and the holographic computation of boundary correlators are automatically implemented in this tensor network.

59 pages, 18 figures; v3: improved presentation, added figures and references

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Cited by in corpus (31)

• Treelike interactions and fast scrambling with cold atoms
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Accurate simulation of q-state clock model
• Scalar fields on $p$AdS
• Surface growth scheme for bulk reconstruction and tensor network
• Wilson line networks in $p$-adic AdS/CFT
• Symmetry Resolution in non-Lorentzian Field Theories
• Holography on local fields via Radon Transform
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Recursion Relations in $p$-adic Mellin Space
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Thread/State correspondence: from bit threads to qubit threads
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• The boundary theory of a spinor field theory on the Bruhat-Tits tree
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Building Archimedean Space
• Bulk-boundary correspondence from hyper-invariant tensor networks
• p-adic CFT is a holographic tensor network
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Effective field theory on a finite boundary of the Bruhat-Tits tree
• From $p$-adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces
• Effective field theories on subspaces of the Bruhat-Tits tree
• Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields
• Absolutely maximally entangled pure states of multipartite quantum systems
• Euclidean (A)dS spaces over $p$-adic numbers
• Massless $p2$-brane modes and the critical line
• A Perfectoid Duality Between M-Theory and F-Theory
• Holographic Aspects of Dynamical Mean-Field Theory