Information metric on the boundary

TL;DR

This paper explores the information metric on boundary conditions in 2D conformal field theories, computing it explicitly for various models and discussing its holographic dual in AdS3/BCFT2 contexts.

Contribution

It provides explicit calculations of the boundary information metric for free boson and SU(2)k WZW theories, and discusses its holographic interpretation in AdS3/BCFT2.

Findings

Computed the boundary information metric for free boson CFT.

Derived the metric for SU(2)k WZW theory, matching symmetry expectations.

Connected the boundary information metric to minimal surface areas in holography.

Abstract

The information metric on the space of boundary coupling constants in two-dimensional conformal field theories is studied. Such a metric is related to the Casimir energy difference of the theory defined on an interval. We concretely compute the information metric on the boundary conformal manifold of free boson CFT as well as SU(2)k WZW theory, obtaining the result expected from the symmetry of the systems. We also compute the information metric on the space of non-conformal boundary states produced by boundary mass perturbations in the theory of a real free scalar. The holographic dual of the boundary information metric in the context of AdS3/BCFT2 is also discussed. We argue that it corresponds to the area of the minimal cross section of the end-of-the-world brane connecting two boundaries of the asymptotic BCFTs.