Interface entropy in four dimensions as Calabi's diastasis on the conformal manifold

TL;DR

This paper proposes a conjecture linking the entropy of Janus interfaces in 4d N=2 superconformal field theories to Calabi's diastasis, a geometric quantity on the conformal manifold.

Contribution

It introduces a novel conjecture connecting interface entropy with Calabi's diastasis in the context of 4d N=2 SCFTs.

Findings

Conjectural equality between interface entropy and Calabi's diastasis.

Provides a geometric interpretation of interface entropy in supersymmetric theories.

Suggests new avenues for understanding moduli space geometry through physical observables.

Abstract

We conjecture an equality between (1) the entropy associated with a Janus interface in a 4d N=2 superconformal field theory and (2) Calabi's diastasis, a particular combination of analytically continued Kahler potentials, on the conformal manifold (moduli space) of the 4d theory.