Holographic Complexity

By M. Alishahiha. 2015

312 citations recorded by the source corpus.

For a field theory with a gravitational dual, following Susskind's proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a co-dimension one time slice in the bulk geometry enclosed by the extremal co-dimension two hyper-surface appearing in the computation of the holographic entanglement entropy. The proportionally constant, up to a numerical order of one factor is G R where G is the Newton constant and R is the curvature of the space time. We study this quantity in certain holographic model. We also explore a possible relation between the defined quantity and fidelity appearing in quantum information literature.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b4a8962bc998cde06630c3edad20ab39a7cde11a

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In Astronomy and Astrophysics

In Nuclear and High Energy Physics

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Citations in the corpus

Comments on holographic complexity (2016, methodology): “These ideas were first considered for time-independent geometries by [21] in the context of CV duality — see also [22].”
Circuit complexity in interacting QFTs and RG flows (2018, unknown): “Moreover from the holographic side [45,87], the corrections due to a relevant deformation using existing holographic proposals have been considered leading to V dependence in the complexity expression.”
Complexity and entanglement for thermofield double states (2018, background): “[24–50], but this research program is still in its nascent stages.”
Circuit complexity in fermionic field theory (2018, background): “One was to understand complexity in quantum field theory as a pre-requisite for understanding holographic complexity [1].”
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, methodology): “For various earlier proposals for holographic subregion complexity refer to [23, 26].”
On the time dependence of holographic complexity (2017, background): “Thus, it is enough to (15)For a proposed generalization for the complexity of subsystems in terms of the co-dimension one volume enclosed by the Ryu-Takayanagi surface, see [27, 45, 46].”
Circuit complexity in quantum field theory (2017, background): “Here our experience with holographic complexity [55] suggests that there may be interesting information that could be extracted from the finite or logarithmic contributions.”
Complexity of formation in holography (2016, background): “See also [44, 45] for proposed generalizations for subregions.”
On volumes of subregions in holography and complexity (2016, methodology): “The case of a sphere in pure AdS was studied in [48].”