Information metric and Euclidean Janus correspondence

TL;DR

This paper explores the duality between the quantum information metric of perturbed conformal field theories and Euclidean Janus geometries, extending the correspondence to higher dimensions and including black hole geometries.

Contribution

It generalizes the duality between the quantum information metric and Janus geometries to higher dimensions and relates mixed-state metrics to Janus black hole geometries.

Findings

Confirmed the duality in higher dimensions.

Established the connection with Janus black hole geometries.

Provided a precise match between field theory and gravity descriptions.

Abstract

We consider the quantum information metric of a family of CFTs perturbed by an exactly marginal operator, which has the dual description of the Euclidean Janus geometries. We first clarify its two dimensional case dual to the three dimensional Janus geometry, which recently appeared in arXiv:1507.07555. We generalize this correspondence to higher dimensions and get a precise agreement between the both sides. We also show that the mixed-state information metric of the same family of CFTs has a dual description in the Euclidean version of the Janus time-dependent black hole geometry.