Information metric and Euclidean Janus correspondence

TL;DR

This work demonstrates a precise holographic match between the quantum information metric for CFTs deformed by an exactly marginal operator and the Euclidean Janus geometries, extending the known 2D/3D duality to higher dimensions. It provides explicit field-theory expressions for $G_{\lambda\lambda}$ and shows the corresponding gravity results agree when the gravity cutoff is related by $\epsilon_0 = 2\epsilon$; it also extends the analysis to mixed-state fidelity, identifying the Euclidean Janus time-dependent black hole as the dual and showing the same $1/\epsilon$-type scaling and cutoff matching. The results reinforce the utility of information-theoretic probes in holography and illuminate how thermal entanglement and thermalization are encoded in Euclidean Janus setups.

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.

Figures (1)

• Figure 1: The conformal shape of the Euclidean time-dependent black hole in ($y,\ \nu$) space is depicted. $y=-\infty$ corresponds to the left semicircle boundary from $B$ and $A$ while $y=\infty$ to the right semi-circle boundary also from $B$ to $A$. The Euclidean time coordinate $\tau$ runs from $B$ to $A$.