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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Complexity and behind the horizon cut off
TL;DR: In this paper, the authors compute holographic complexity for a black brane solution with a cutoff using the complexity=action proposal, which is in contrast with the naively computation which is done without assuming the cutoff where the complexity approaches a constant at the late time.
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Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
TL;DR: In this article, the authors examined the holographic complexity in the doubly holographic model and derived the leading contributions to the complexity and interpreted these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the brane.
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Complexity growth of operators in the SYK model and in JT gravity
TL;DR: In this paper, the authors study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in JT gravity.
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Entanglement Entropy in a Holographic Kondo Model
TL;DR: In this paper, entanglement and impurity entropies in a recent holographic model of a magnetic impurity interacting with a strongly coupled system were calculated according to the Ryu-Takayanagi prescription.
References
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