General bounds on holographic complexity

Engelhardt, Netta; Folkestad, Åsmund

doi:10.1007/jhep01(2022)040

Title: General bounds on holographic complexity

Journal Article · 09 January 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)040 · OSTI ID:1864710

Engelhardt, Netta ^[1];

^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Massachusetts Institute of Technology
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0021886; SC0012567

OSTI ID:: 1864710

Report Number(s):: MIT-CTP/5329

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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