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General Bounds on Holographic Complexity

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arxiv 2109.06883 v1 pith:O3A7JBP7 submitted 2021-09-14 hep-th gr-qc

Netta Engelhardt , {AA}smund Folkestad This is my paper · ORCID
classification hep-thgr-qc
keywords volumecomplexityenergyholographicpositivetheorembulkcondition
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We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd's bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Holographic Time Crystals vs Penrose

    hep-th 2025-02 conditional novelty 7.0 of 10

    In spherically symmetric Einstein-scalar gravity with conformally invariant boundary conditions, the AdS Penrose inequality holds exactly when a positive mass theorem holds, ruling out neutral, non-rotating holographi...

  2. Spread complexity for the planar limit of holography

    hep-th 2024-12 reject novelty 6.0 of 10

    Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.

  3. Wedge Holographic Complexity in Karch-Randall Braneworld

    hep-th 2024-12 conditional novelty 6.0 of 10

    For a wedge black string with fluctuating branes, the Complexity=Action growth rate gains a constant edge-mode term while Complexity=Volume gains a fluctuation-squared correction, breaking the naive equivalence of the...

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