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Subregion Action and Complexity
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Subregion Action and Complexity
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We evaluate finite part of the on-shell action for black brane solutions of Einstein gravity on different subregions of spacetime enclosed by null boundaries. These subregions include the intersection of WDW patch with past/future interior and left/right exterior for a two sided black brane. Identifying the on-shell action on the exterior regions with subregion complexity one finds that it obeys subadditivity condition. This gives an insight to define a new quantity named mutual complexity. We will also consider certain subregion that is a part of spacetime which could be causally connected to an operator localized behind/outside the horizon. Taking into account all terms needed to have a diffeomorphism invariant action with a well-defined variational principle, one observes that the main contribution that results to a nontrivial behavior of the on-shell action comes from joint points where two lightlike boundaries (including horizon) intersect. A spacelike boundary gives rise to a linear time growth, while we have a classical contribution due to a timelike boundary that is given by the free energy.
Forward citations
Cited by 8 Pith papers
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Complexity Inequalities for Quantum Subsystems
Introduces tripartite complexity and complexity gap for three-region subsystems and reports that the gap has a definite sign in holographic volume complexity, Fisher-Rao Gaussian complexity, and Krylov-space approaches.
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for comp...
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Combinatorial aspects of holographic quantum secret sharing
Bulk regions in AdS3/CFT2 get a holographic secret-sharing distance d and thresholds (r,s), with r = n - d + 1; pure states satisfy s = d - 1 while mixed states can satisfy s >= d.
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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.
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Timelike Holographic Complexity
Timelike subregion complexity within the holographic Complexity=Volume conjecture is computed for pure AdS and AdS black branes; it is purely real and shares the spacelike UV divergence structure.
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The Entanglement Wedge Polygon
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
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Entanglement Entropy and Complexity of Multicomponent Universe from Holography
For two-component FLRW universes built from an AdS black brane plus p-brane gas, holographic entanglement entropy scales as tau early and as tau^{4/3} (dark matter) or tau^2 (exotic matter) late, while volume complexi...
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Holographic entanglement entropy and complexity for the cosmological braneworld model
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane...
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