Holographic Complexity Equals Bulk Action?

• Main Authors: Brown, Adam R. (Author), Susskind, Leonard (Author), Swingle, Brian (Author), Zhao, Ying (Author), Roberts, Daniel Adam (Contributor)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2016-05-12T01:35:50Z.
• Subjects: Article
• Online Access: Get fulltext

We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch. We illustrate and test the conjecture in the context of neutral, charged, and rotating black holes in anti-de Sitter spacetime, as well as black holes perturbed with static shells and with shock waves. This conjecture evolved from a previous conjecture that complexity is dual to spatial volume, but appears to be a major improvement over the original. In light of our results, we discuss the hypothesis that black holes are the fastest computers in nature.
Hertz Foundation
United States. Dept. of Energy (Cooperative Research Agreement Contract DE-SC0012567)