Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories

TL;DR

This paper demonstrates that the entropy of Janus interfaces in 4d $ N=2$ superconformal field theories is proportional to Calabi's diastasis, linking geometric properties of the coupling space to entanglement entropy.

Contribution

It establishes a direct relation between Janus interface entropy and Calabi's diastasis in 4d $ N=2$ SCFTs, confirming and generalizing previous conjectures.

Findings

Janus interface entropy is proportional to Calabi's diastasis.

The relation is derived using conformal mapping techniques.

The result generalizes earlier 2D findings.

Abstract

We study the entropy associated with the Janus interface in a 4$d$ $\mathcal{N}=2$ superconformal field theory. With the entropy defined as the interface contribution to an entanglement entropy we show, under mild assumptions, that the Janus interface entropy is proportional to the geometric quantity called Calabi's diastasis on the space of $\mathcal{N}=2$ marginal couplings, confirming an earlier conjecture by two of the authors and generalizing a similar result in two dimensions. Our method is based on a CFT consideration that makes use of the Casini-Huerta-Myers conformal map from the flat space to the round sphere.