Gravity Dual of Quantum Information Metric

TL;DR

This paper explores the gravity dual of the quantum information metric in conformal field theories, proposing it corresponds to the volume of a maximal time slice in AdS spacetime, especially for marginal perturbations, and confirms this through examples.

Contribution

It introduces a gravity dual description of the quantum information metric as a maximal volume in AdS, extending the holographic understanding of quantum information measures.

Findings

Quantum information metric relates to maximal volume in AdS for marginal perturbations.

The proposed duality is confirmed through multiple example calculations.

Provides a geometric interpretation of fidelity susceptibility in holography.

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.