Holographic Complexity Equals Bulk Action
TLDR
The hypothesis that black holes are the fastest computers in nature is discussed and the conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that is called a Wheeler-DeWitt patch is illustrated.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.read more
Citations
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Time evolution of the complexity in chaotic systems: a concrete example
TL;DR: In this paper, the authors investigated the time evolution of the complexity of the operator by the SYK model with N Majorana fermions and showed that the bi-invariant complexity may be a competitive candidate for the complexity in quantum mechanics/field theory.
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Complexity and Near Extremal Charged Black Branes
TL;DR: In this article, the holographic complexity of charged black brane solutions in arbitrary dimensions for the near horizon limit of near extremal case using two different methods was computed, and the corresponding complexity may be obtained either by taking the limit from the complexity of the charged brane, or by computing the complexity for near-horizon limit of NE solution.
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More on complexity of operators in quantum field theory
TL;DR: In this paper, the complexity of SU($n$) operator in a bi-invariant Finsler geometry was shown to be determined by the geodesic length of the topology and curvature of the sectional curvature.
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Does Complexity Equal Anything?
TL;DR: In this paper , a new infinite class of gravitational observables in asymptotically anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice, is presented.
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Holographic complexity and thermodynamics of AdS black holes
TL;DR: In this article, it was shown that the complexity growth rate at late times is equal to temperature times black hole entropy, and that the result holds at lower temperatures as well for AdS planar black holes.
References
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