Holographic Complexity Equals Bulk Action?
By Adam R. Brown, Daniel A. Roberts, L. Susskind, Brian Swingle, Ying Zhao. Physical Review Letters, 2015
786 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c9b3f6b7eca4d47f7bec39a72700c52d9ad2acbf
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Citations in the corpus
- Holographic complexity in Vaidya spacetimes. Part I (2018, background): “29) is always smaller than the corresponding result [29, 30] for the eternal black hole geometry with any d and for both k = 0 and +1.”
- Onset of many-body chaos in the $O(N)$ model (2017, background): “After the system is effectively scrambled, the quantum state continues to move in Hilbert space and can continue to grow in complexity up to extremely long times [18].”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “On a related note, one might also study the complexity of these brane configurations, for example, using the higher-dimensional bulk to probe holographic complexity conjectures [145–148], e.”
- Comments on holographic complexity (2016, background): “The CA duality [9, 10] requires evaluating the gravitational action for a bulk spacetime region with null boundaries.”
- Action growth for AdS black holes (2016, methodology): “This explains why the authors of [8, 19] could find the saturated bound (1.”
- Quantum complexity and negative curvature (2016, background): “In particular, this functional form will be true if we use ERB volume [1, 3] or action [12, 13].”
- The Black Hole Information Problem (2016, background): “Finally, for your interest, I mention the work [74], which goes beyond chaos to complexity.”
- Circuit complexity in quantum field theory (2017, background): “This identifies the complexity of the boundary state with the gravitational action evaluated on a bulk region known as the Wheeler-DeWitt (WDW) patch [15, 16]:”
- The quantum gravity dynamics of near extremal black holes (2018, background): “Using the complexity equal to volume conjecture [28, 29], the complexity of thermofield double state is proportional to the maximum volume: C(t) = #V(t) = # β .”
- Circuit complexity for coherent states (2018, background): “In particular, there are two proposals for ‘holographic complexity’: complexity=volume (CV) [15, 16] and complexity=action (CA) [17, 18].”
- On volumes of subregions in holography and complexity (2016, background): “This result led to the very interesting conjecture [25, 26, 47] that black holes saturate the inequality:”
- Krylov complexity in conformal field theory (2021, background): “At the level of definition it is not related to circuit complexity, but a number of recent works [10–12] found qualitative agreement between the behavior of KO(t) with the behavior of circuit and holographic complexities [13].”