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Hot multiboundary wormholes from bipartite entanglement

Donald M. Marolf, Henry Maxfield, Alex Peach, Simon F. Ross

Published Oct 8, 2015• 33 citations
OpenAlex

Abstract

We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, -rfnet≥1 asymptotically-AdS3 regions, and arbitrary internal topology. The dual state at t = 0 is defined on n circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points (vertices) any small connected region A of the boundary CFT is entangled only with another small connected region B, where B may lie on a different circle or may be a different part of the same circle. We focus on the pair-of-pants case, from which more general cases may be constructed. We also discuss finite-temperature corrections, where we note that the states involve a code subspace in each circle.

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We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, -rfnet≥1 asymptotically-AdS3 regions, and arbitrary internal topology. The dual state at t = 0 is defined on n circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points (vertices) any small connected region A of the boundary CFT is entangled only with another small connected region B, where B may lie on a different circle or may be a different part of the same circle. We focus on the pair-of-pants case, from which more general cases may be constructed. We also discuss finite-temperature corrections, where we note that the states involve a code subspace in each circle.
Abstract We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, asymptotically-AdS 3 regions, and arbitrary internal topology. The dual state at t = 0 is defined on n circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points (‘vertices’) any small connected region A of the boundary CFT is entangled only with another small connected region B , where B may lie on a different circle or may be a different part of the same circle. We focus on the pair-of-pants case, from which more general cases may be constructed. We also discuss finite-temperature corrections, where we note that the states involve a code subspace in each circle.
The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS_3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, in some regions of the moduli space the entanglement is almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between at least n-1 parties, and that the distillable entanglement between the asymptotic regions is at least (n+1)/2 partite.
The AdS/CFT correspondence relates quantum entanglement between boundary conformal field theories and geometric connections in the dual asymptotically anti-de Sitter spacetime. We consider entangled states in the n-fold tensor product of a 1 + 1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, there are regions of the moduli space in which the entanglement is instead almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between all n parties, and that the distillable entanglement between the asymptotic regions is at least (n + 1)/2 partite.
We calculate the topological entanglement entropy (TEE) in Euclidean asymptotic AdS3 spacetime using surgery. The treatment is intrinsically three-dimensional. In the BTZ black hole background, several different bipartitions are applied. For the bipartition along the horizon between two single-sided black holes, TEE is exactly the Bekenstein-Hawking entropy, which supports the ER=EPR conjecture in the Euclidean case. For other bipartitions, we derive an Entangling-Thermal relation for each single-sided black hole, which is of topological origin. After summing over genus-one classical geometries, we compute TEE in the high-temperature regime. In the case where k = 1, we find that TEE is the same as that for the Moonshine double state, given by the maximally-entangled superposition of 194 types of “anyons” in the 3d bulk, labeled by the irreducible representations of the Monster group. We propose this as the bulk analogue of the thermofield double state in the Euclidean spacetime. Comparing the TEEs between thermal AdS3 and BTZ solutions, we discuss the implication of TEE on the Hawking-Page transition in 3d.
Abstract We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.
Using gauge/gravity duality, we explore a class of states of two CFTs with a large degree of entanglement, but with very weak local two-sided correlation. These states are constructed by perturbing the thermofield double state with thermal-scale operators that are local at different times. Acting on the dual black hole geometry, these perturbations create an intersecting network of shock waves, supporting a very long wormhole. Chaotic CFT dynamics and the associated fast scrambling time play an essential role in determining the qualitative features of the resulting geometries.