Surface/state correspondence as a generalized holography

Miyaji, Masamichi; Takayanagi, Tadashi

doi:10.1093/ptep/ptv089

Cited by 188 publications

(247 citation statements)

References 49 publications

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“…For other approaches of entanglement based renormalization group, see refs. [21][22][23][24]. In the present case, the disentangler e −zĤ is a non-unitary operator.…”

Section: Jhep09(2016)044mentioning

confidence: 78%

Horizon as critical phenomenon

Lee

2016

J. High Energ. Phys.

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We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

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“…For other approaches of entanglement based renormalization group, see refs. [21][22][23][24]. In the present case, the disentangler e −zĤ is a non-unitary operator.…”

Section: Jhep09(2016)044mentioning

confidence: 78%

Horizon as critical phenomenon

Lee

2016

J. High Energ. Phys.

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“…Tensor network renormalization (TNR) is a procedure to reorganize the tensors to ones on a coarser lattice by inserting projectors (isometries) and unitaries (disentanglers) with removing short-range entanglement. 9 This is a step of TNR (figure 4). Repeating this procedure, we can generate a RG flow properly JHEP11(2017)097 and end up with a tensor network at the IR fixed point.…”

Section: Tensor Network Renormalization and Optimizationmentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

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285

402

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Abstract:We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

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“…The recently proposed duality called surface/state correspondence [3] gives a more detailed structure of holographic relations. This duality can in principle be applied to any spacetimes described by Einstein gravity and even to those without time-like boundaries.…”

Section: Introductionmentioning

confidence: 99%

“…just a point. Such a state dual to a point in a gravitational spacetime is identified with the boundary state |B [3]. This is because there is no real space entanglement for the state dual to such a point-like surface, according to the idea of holographic entanglement entropy [12], and because the state with a vanishing real space entanglement entropy is given by the boundary state [13].…”

Section: Introductionmentioning

confidence: 99%

Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

et al. 2015

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We present how the surface/state correspondence, conjectured in arXiv:1503.03542, works in the setup of AdS3/CFT2 by generalizing the formulation of cMERA. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on AdS3 and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it is given by that of 2d hyperbolic manifold, which is argued to describe the time slice of AdS3.

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Surface/state correspondence as a generalized holography

Cited by 188 publications

References 49 publications

Horizon as critical phenomenon

Horizon as critical phenomenon

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

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