Complexity of Jackiw-Teitelboim gravity

• Published in: Physical Review D
• Main Authors: Brown, Adam R., Gharibyan, Hrant, Lin, Henry W., Susskind, Leonard, Thorlacius, Larus, Zhao, Ying
• Other Authors: Raunvísindastofnun (HÍ), Science Institute (UI), Verkfræði- og náttúruvísindasvið (HÍ), School of Engineering and Natural Sciences (UI), Háskóli Íslands, University of Iceland
• Format: Article in Journal/Newspaper
• Language: English
• Published: American Physical Society (APS) 2019
• Subjects: Jackiw-Teitelboim; Black holes; Wheeler-DeWitt patch; Svarthol (stjörnufræði); Líkön; DeWitt; Iceland
• Online Access: https://hdl.handle.net/20.500.11815/1804; https://doi.org/10.1103/PhysRevD.99.046016

Publisher's version (útgefin grein) The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes. Motivated by the holographic complexity conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surprisingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact agreement with expectations. We comment on the general lessons that this might hold for holographic complexity and beyond. We are grateful to Kurt Hinterbichler, Fedor Popov, Douglas Stanford, and Alexandre Streicher. We would especially like to thank Hugo Marrochio for communicating to us the results of [20]. This research was supported by the John Templeton Foundation (A. B.), by the NDSEG program (H. L.), by NSF Grant No. PHY-1720397 (H. G.), by NSF Grant No. 1316699 (L. S.), by the Icelandic Research Fund under Grant No. 163422-053 and the University of Iceland Research Fund (L. T.), and by the Simons Foundation (Y. Z.). Peer Reviewed