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Complexity and Momentum · Around

2020

Complexity and Momentum

Susskind, Leonard, Zhao, Ying

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Previous work has explored the connections between three concepts -- operator size, complexity, and the bulk radial momentum of an infalling object -- in the context of JT gravity and the SYK model.

In this paper we investigate the higher dimensional generalizations of these connections.
We use a toy model to study the growth of an operator when perturbing the vacuum of a CFT.
From circuit analysis we relate the operator growth to the rate of increase of complexity and check it by complexity-volume duality.

Built on

L. Susskind, “Complexity and Newton’s Laws,” [arXiv:1904.12819 [hep-th]]
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H. W. Lin, J. Maldacena and Y. Zhao, “Symmetries Near the Horizon,” JHEP 08
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B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
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Then

A. R. Brown, H. Gharibyan, A. Streicher, L. Susskind, L. Thorlacius and Y. Zhao, “Falling Toward Charged Black Holes,” Phys. Rev. D 98
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2018
Later among the works it cites.
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2018
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Y. Zhao, “Complexity and Boost Symmetry,” Phys. Rev. D 98
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2018
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X. Qi and A. Streicher, “Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK,” JHEP 08
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2019
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Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP 10
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2016

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L. Susskind, “Why do Things Fall?,” [arXiv:1802.01198 [hep-th]]

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L. Susskind and Y. Zhao, “Switchbacks and the Bridge to Nowhere,” arXiv:1408.2823 [hep-th]

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B. Swingle, “Constructing holographic spacetimes using entanglement renormalization,” [arXiv:1209.3304 [hep-th]]

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L. Susskind and E. Witten, “The Holographic bound in anti-de Sitter space,” [arXiv:hep-th/9805114 [hep-th]]

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2096

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