Gravity Dual of Quantum Information Metric

Abstract

We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

5 pages plus appendices, Revtex, 2 figures

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• Complexity and Shock Wave Geometries
• Surface/State Correspondence as a Generalized Holography
• cMERA as Surface/State Correspondence in AdS/CFT

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