A geometrical representation of the quantum information metric in the gauge/gravity correspondence

TL;DR

This paper explores how the quantum information metric, which quantifies the distance between ground states in field theories, can be geometrically represented in the gauge/gravity duality, linking it to surface volume changes in gravity.

Contribution

It demonstrates that the quantum information metric corresponds to a back reaction on the volume of a codimension-2 surface in gravity for theories with Poincare symmetry.

Findings

Quantum information metric linked to surface volume changes in gravity

Back reaction on codimension-2 surface encodes state differences

Applicable to theories with Poincare symmetry

Abstract

We study a geometrical representation of the quantum information metric in the gauge/gravity correspondence. We consider the quantum information metric that measures the distance between the ground states of two theories on the field theory side, one of which is obtained by perturbing the other. We show that the information metric is represented by a back reaction to the volume of a codimension-2 surface on the gravity side if the unperturbed field theory possesses the Poincare symmetry.