Holographic duality from random tensor networks
Reviewed by Pithpith:UE6BHRMUopen to challenge →
read the original abstract
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface topologically in a way similar to creation of a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by AdS/CFT duality, our main results define a more general form of bulk-boundary correspondence which could be useful for extending holography to other spacetimes.
This paper has not been read by Pith yet.
Forward citations
Cited by 17 Pith papers
-
Replica wormholes and the black hole interior
Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
-
Multi-entropy in random tensor networks
For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
-
Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
-
Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks are introduced as a class satisfying computational covariance, bounding complexity by the Python's Lunch Conjecture exponent, and combining holographic features of perfect and random te...
-
Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
-
Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
-
Logarithmic negativity typically equals exact entanglement cost
Logarithmic negativity equals exact entanglement cost under PPT-preserving operations for large random induced mixed states.
-
Subregion observer rules from generalized entanglement wedges
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
-
The Entanglement Wedge Polygon
The paper defines the entanglement wedge polygon as the intersection of entanglement wedges external to individual homology regions and studies its topological and geometric properties in AdS examples.
-
Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group in the Massless Critical Limit
Functional renormalization group applied to the O(N) vector model generates an emergent regular AdS_{d+1} geometry whose near-horizon thermodynamics reproduces the first law and Bekenstein-Hawking area law with temper...
-
A Semiclassical Diagnostic for Spacetime Emergence
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
-
Holographic Tensor Networks as Tessellations of Geometry
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
-
Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry
Spectral bounds relate graph Laplacian eigenvalues to the congestion of binary-tree embeddings, with an efficient spectral-ordering algorithm and applications to tensor-network contraction complexity.
-
Holography and Kinematic Space for Gravitational Sub-regions in AdS
Extends kinematic space and PEE threads to subregions in AdS and builds tensor networks on them realizing surface-state correspondence for gravitational subregions.
-
Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group in the Massless Critical Limit
Functional renormalization group flow of the O(N) vector model produces an emergent AdS_{d+1} geometry under the massless critical condition.
-
The Junction Law for Multipartite Entanglement in Confining Holographic Backgrounds
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.
-
Channel-State duality with centers
Generalizes channel-state duality to algebras with centers, establishing a link between state non-separability and channel isometry, plus extension to infinite-dimensional trace-class operators.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.