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Action growth for AdS black holes

Journal of High Energy Physics volume 2016, Article number: 161 (2016) Cite this article

A preprint version of the article is available at arXiv.

Abstract

Recently a Complexity-Action (CA) duality conjecture has been proposed, which relates the quantum complexity of a holographic boundary state to the action of a Wheeler-DeWitt (WDW) patch in the anti-de Sitter (AdS) bulk. In this paper we further investigate the duality conjecture for stationary AdS black holes and derive some exact results for the growth rate of action within the Wheeler-DeWitt (WDW) patch at late time approximation, which is supposed to be dual to the growth rate of quantum complexity of holographic state. Based on the results from the general D-dimensional Reissner-Nordström (RN)-AdS black hole, rotating/charged Bañados-Teitelboim-Zanelli (BTZ) black hole, Kerr-AdS black hole and charged Gauss-Bonnet-AdS black hole, we present a universal formula for the action growth expressed in terms of some thermodynamical quantities associated with the outer and inner horizons of the AdS black holes. And we leave the conjecture unchanged that the stationary AdS black hole in Einstein gravity is the fastest computer in nature.

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Authors and Affiliations

  1. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, No. 55 Zhong Guan Cun East Street, Beijing, 100190, China

    Rong-Gen Cai, Shan-Ming Ruan, Shao-Jiang Wang, Run-Qiu Yang & Rong-Hui Peng

  2. School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China

    Rong-Gen Cai, Shan-Ming Ruan, Shao-Jiang Wang, Run-Qiu Yang & Rong-Hui Peng

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  1. Rong-Gen Cai
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  2. Shan-Ming Ruan
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Correspondence to Shao-Jiang Wang.

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ArXiv ePrint: 1606.08307

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Cai, RG., Ruan, SM., Wang, SJ. et al. Action growth for AdS black holes. J. High Energ. Phys. 2016, 161 (2016). https://doi.org/10.1007/JHEP09(2016)161

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  • DOI: https://doi.org/10.1007/JHEP09(2016)161

Keywords

  • Black Holes
  • AdS-CFT Correspondence
  • Conformal Field Theory