title: Holographic Complexity Equals Bulk Action?
abstract: 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.
authors.affiliation: Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Adam R
authors.initials: AR
authors.lastname: Brown
authors.affiliation: Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Roberts
authors.affiliation: Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Leonard
authors.initials: L
authors.lastname: Susskind
authors.affiliation: Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Brian
authors.initials: B
authors.lastname: Swingle
authors.affiliation: Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Ying
authors.initials: Y
authors.lastname: Zhao