Holographic complexity

Alishahiha, Mohsen

doi:10.1103/physrevd.92.126009

Cited by 287 publications

(479 citation statements)

References 42 publications

(75 reference statements)

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“…In summary, we obtain the relative actions: 27) which indeed satisfy (6.13). When a = 1, they are reduced to (6.19), (6.20), (6.21).…”

Section: Jhep11(2017)097mentioning

confidence: 66%

“…[34][35][36][37][38][39][40][41][42]). We would also like to mention that for CFTs, the behavior of the complexity is very similar to the quantum information metric under marginal deformations as pointed out in [43] (refer to [27,31,44] for recent developments), where the metric is argued to be well approximated by the volume of maximal time slice in AdS.…”

Section: Jhep11(2017)097mentioning

confidence: 70%

“…Secondly, in the tensor network description there is a subtle issue that the MERA network can also be interpreted as a de Sitter space [6,11], while the refined tensor networks given in [10,13] are argued to describe Euclidean 2 The relevance of computational complexity in holography was recently pointed out and holographic complexity was conjectured to be the volume of maximal time slice in gravity duals [25,26] (for recent progresses see e.g. [27][28][29][30][31]) and the gravity action in Wheeler-De Witt patch in [32,33] (for recent progresses see e.g. [34][35][36][37][38][39][40][41][42]).…”

Section: Jhep11(2017)097mentioning

confidence: 99%

“…It is natural to argue that this provides a definition of complexity for the reduced density matrix ρ A . For various earlier proposals for holographic subregion complexity refer to [27,30].…”

Section: Subregion Complexitymentioning

confidence: 99%

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

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

281

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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“…In summary, we obtain the relative actions: 27) which indeed satisfy (6.13). When a = 1, they are reduced to (6.19), (6.20), (6.21).…”

Section: Jhep11(2017)097mentioning

confidence: 66%

Section: Jhep11(2017)097mentioning

confidence: 70%

Section: Jhep11(2017)097mentioning

confidence: 99%

Section: Subregion Complexitymentioning

confidence: 99%

See 2 more Smart Citations

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

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

281

402

View full text Add to dashboard Cite

show abstract

“…The renormalized quantum information metric is well defined physically and can be measured experimentally in principle. Since we now have definite predictions for the quantum information metric, our results can be used to clarify a possible relation between the quantum information metric and other quantities like quantum complexity [12][13][14][15].…”

Section: Discussionmentioning

confidence: 81%

Quantum information metric on ℝ × S d − 1

Bak

Trivella²

2017

J. High Energ. Phys.

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We present a formula for the information metric on R × S d−1 for a scalar primary operator of integral dimension ∆ ( > d+12 ). This formula is checked for various space-time dimensions d and ∆ in the field theory side. We check the formula in the gravity side using the holographic setup. We clarify the regularization and renormalization involved in these computations. We also show that the quantum information metric of an exactly marginal operator agrees with the leading order of the interface free energy of the conformal Janus on Euclidean S d , which is checked for d = 2, 3.

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Entanglement entropy in a holographic Kondo model

Erdmenger

Flory

Hoyos

et al. 2016

Fortschritte der Physik

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We calculate entanglement and impurity entropies in a recent holographic model of a magnetic impurity interacting with a strongly coupled system. There is an RG flow to an IR fixed point where the impurity is screened, leading to a decrease in impurity degrees of freedom. This information loss corresponds to a volume decrease in our dual gravity model, which consists of a codimension one hypersurface embedded in a BTZ black hole background in three dimensions. There are matter fields defined on this hypersurface which are dual to Kondo field theory operators. In the large N limit, the formation of the Kondo cloud corresponds to the condensation of a scalar field. The entropy is calculated according to the Ryu-Takayanagi prescription. This requires to determine the backreaction of the hypersurface on the BTZ geometry, which is achieved by solving the Israel junction conditions. We find that the larger the scalar condensate gets, the more the volume of constant time slices in the bulk is reduced, shortening the bulk geodesics and reducing the impurity entropy. This provides a new non-trivial example of an RG flow satisfying the g-theorem. Moreover, we find explicit expressions for the impurity entropy which are in agreement with previous field theory results for free electrons. This demonstrates the universality of perturbing about an IR fixed point.Dedicated to the memory of our colleague Peter Breitenlohner

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Holographic complexity

Cited by 287 publications

References 42 publications

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

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

Quantum information metric on ℝ × S d − 1

Entanglement entropy in a holographic Kondo model

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