Rong-Hui Peng | Searcharxiv

arXiv2018

The effect of Dilaton on the holographic complexity growth

In this paper, we investigate the action growth in various backgrounds in Einstein-Maxwell-Dilaton theory. We calculate the full time evolution of action growth in AdS dilaton black hole and find it approaches the late time bound from above. We investigate the black hole which is asymptotically Lifshitz and obtain its late-time and full time behavior. We find the violation of Lloyd bound in late time limit and show the full time behavior exhibiting some new features for z sufficiently large.

hep-th↗

arXiv2016

Complexity Growth for AdS Black Holes

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.

gr-qc↗