Holographic Complexity Equals Bulk Action?

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.

• NS
  National Science Foundation

  Award: 0756174
• UD
  U.S. Department of Energy

  Award: DE-SC00012567
• SF
  Simons Foundation
• JT
  John Templeton Foundation
• HF
  Hertz Foundation
• IP
  Institut Périmètre de physique théorique