Holographic Computations of the Quantum Information Metric

TL;DR

This paper demonstrates how to compute the Quantum Information Metric holographically through a perturbative scalar field approach, applying it to specific CFT states and generalizing to multi-dimensional parameter spaces.

Contribution

It introduces a perturbative holographic method for calculating the Quantum Information Metric, including a generalization to multi-dimensional parameter spaces and its relation to non-linear sigma models.

Findings

Quantum Information Metric can be computed holographically using scalar perturbations.

The method applies to ground states and thermofield double states deformed by operators.

The Quantum Information Metric matches the metric of a non-linear sigma model in multi-parameter cases.

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.