Comments on fusion matrix in N=1 super Liouville field theory

TL;DR

This paper investigates the fusion matrix in N=1 super Liouville theory, revealing structural similarities with rational conformal field theory and constructing defects via Cardy-Lewellen equations.

Contribution

It provides new insights into the fusion matrix structure in super Liouville theory and extends relations to the Ramond sector, including defect construction.

Findings

Fusion matrix elements relate to structure constants similarly to rational CFT.

Evidence suggests these relations extend to the Ramond sector.

Constructed defects using Cardy-Lewellen equations.

Abstract

We study several aspects of the $N=1$ super Liouville theory. We show that certain elements of the fusion matrix in the Neveu-Schwarz sector related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy-Lewellen equation for defects is studied, and defects are constructed.