Holographic Computations of the Quantum Information Metric

Abstract

In this note we show how the Quantum Information Metric can be computed holographically using a perturbative approach. In particular when the deformation of the conformal field theory state is induced by a scalar operator the corresponding bulk configuration reduces to a scalar field perturbatively probing the unperturbed background. We study two concrete examples: a CFT ground state deformed by a primary operator and thermofield double state in $d=2$ deformed by a marginal operator. Finally, we generalize the bulk construction to the case of a multi dimensional parameter space and show that the Quantum Information Metric coincides with the metric of the non-linear sigma model for the corresponding scalar fields.

21 pages, 5 figures

References in corpus (3)

• Entanglement density and gravitational thermodynamics
• A note on entanglement entropy and regularization in holographic interface theories
• Conformal Janus on Euclidean Sphere

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