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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Testing holographic conjectures of complexity with Born–Infeld black holes
Jun Tao,Peng Wang,Haitang Yang +2 more
TL;DR: In this article, the authors used Born-Infeld black holes to test two holographic conjectures of complexity, the Complexity = Action (CA) duality and the Complexity = Volume 2.0 duality.
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Holographic subregion complexity under a thermal quench
TL;DR: In this paper, the subregion complexity in the CFT is captured by the volume of the codimension-one surface enclosed by the two extremal entanglement surface and the boundary subregion.
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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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De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity
TL;DR: In this paper, the authors investigated the connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and showed that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel.
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Thoughts on holographic complexity and its basis dependence
TL;DR: In this article, the authors argue that holographic complexity should be a basis-dependent quantity, i.e., it is not invariant under a change of the basis of the Hilbert space.
References
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The world as a hologram
TL;DR: In this article, the effects of particle growth with momentum on information spreading near black hole horizons were investigated. But the authors only considered the earliest times of the propagation of information near the horizon.
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TL;DR: In this article, the authors used holography to study sensitive dependence on initial conditions in strongly coupled field theories and showed that the effect of the early infalling quanta relative to the t = 0 slice creates a shock wave that destroys the local two-sided correlations present in the unperturbed state.
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TL;DR: In this paper, an upper bound on the strength of gravity relative to gauge forces in quantum gravity was given, motivated by arguments involving holography and absence of remnants, the stability of black holes as well as the non-existence of global symmetries in string theory.
Dimensional reduction in quantum gravity
TL;DR: In this article, Abdus Salam argued that the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time.