Janus interface in two-dimensional supersymmetric gauge theories

TL;DR

This paper investigates the Janus interface in 2D N=(2,2) supersymmetric gauge theories, demonstrating how small coupling variations relate to sphere partition functions and proposing methods for larger variations, linking to A-model correlators.

Contribution

It provides an analytic continuation approach for Janus partition functions and connects interface entropy to Calabi's diastasis, extending understanding of supersymmetric interfaces.

Findings

Sphere partition function analytically continued for small coupling variations.

Interface entropy proportional to Calabi's diastasis.

Janus partition function for equivariant A-twist generates A-model correlators.

Abstract

We study the Janus interface, a domain wall characterized by spatially varying couplings, in two-dimensional N=(2,2) supersymmetric gauge theories on the two-sphere. When the variations of the couplings are small enough, SUSY localization in the Janus background gives an analytic continuation of the sphere partition function. This directly demonstrates that the interface entropy is proportional to the quantity known as Calabi's diastasis, as originally shown by Bachas et al. When the variations are not small, we propose that an analytic continuation of the sphere partition function coincides with the Janus partition function. We give a prescription for performing such analytic continuation and computing monodromies. We also point out that the Janus partition function for the equivariant A-twist is precisely the generating function of A-model correlation functions.