Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

Abstract

Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in $Ad{S}_{2+1}$ are explored and several important properties are obtained. These properties allow us, via the RFS/HC duality, to obtain a set of remarkable identities of the reduced fidelity susceptibility, which may have significant implications for our understanding of the reduced fidelity susceptibility. Moreover, utilizing these properties and the recent proposed diagnostic tool based on the fidelity susceptibility, experimental verification of the RFS/HC duality becomes possible.

16 pages, 5 figures, references added

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• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• On subregion holographic complexity and renormalization group flows
• Holographic complexity of the disk subregion in (2+1)-dimensional gapped systems
• Holographic subregion complexity of a 1+1 dimensional $p$-wave superconductor
• Quantum information metric of conical defect
• Complexity growth for topological black holes by holographic method
• Thermodynamic and Holographic Information Dual to Volume
• Interface in AdS black hole spacetime
• Holographic complexity for nonlinearly charged Lifshitz black holes
• Holographic Entanglement Entropy, Complexity, Fidelity Susceptibility and Hierarchical UV/IR Mixing Problem in $AdS_2/\mbox{open strings}$
• Holographic complexity of black non-susy D3-brane and the high temperature limit
• On Complexity of Holographic Flavors
• D5-brane on topological black holes
• Interface in Kerr-AdS black hole spacetime
• Quantum Information metric for time-dependent quantum systems and higher-order corrections