Calabi's diastasis as interface entropy

We show that the entropy of certain conformal interfaces between $N=(2,2)$ sigma models that belong to the same moduli space, has a natural geometric interpretation in the large volume limit as Calabi's diastasis function. This is an extension of the well-known relation between the quantum K\"ahler potential and the overlap of canonical Ramond-Ramond ground states in $N=(2,2)$ models.