Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane

Abstract

We examine holographic complexity in the doubly holographic model introduced in [arXiv:2006.04851][arXiv:2010.00018] to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the brane. Motivated by these results, we propose a generalization of the CV proposal for higher curvature theories of gravity. Further, we provide two consistency checks of our proposal by studying Gauss-Bonnet gravity and f(R) gravity in the bulk.

45+5pages, 5 figures

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Cited by in corpus (11)

• Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
• Defect extremal surface as the holographic counterpart of Island formula
• Black holes in dS${}_3$
• AdS/BCFT with Brane-Localized Scalar Field
• Submerging islands through thermalization
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• Holographic and QFT Complexity with angular momentum
• Circumventing the black hole hair-loss problem