Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2022)040
Keywords
AdS-CFT Correspondence; Black Holes; Gauge-gravity correspondence
Categories
Funding
- NSF [PHY-2011905]
- MIT department of physics
- U.S. Department of Energy, Office of Science, Office of High Energy Physics of U.S. Department of Energy [DE-SC0012567]
- U.S. Department of Energy Early Career Award [DE-SC0021886]
- Aker Scholarship
- U.S. Department of Energy (DOE) [DE-SC0021886] Funding Source: U.S. Department of Energy (DOE)
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We prove a positive volume theorem for asymptotically AdS spacetimes and a positive holographic complexity theorem under the Complexity=Volume proposal. We also provide a holographic proof of Lloyd's bound for a class of bulk spacetimes and establish a partial rigidity result for wormholes.
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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