A common limit of super Liouville theory and minimal models

TL;DR

This paper demonstrates that N=1 supersymmetric Liouville theory and supersymmetric minimal models converge to a common non-rational superconformal field theory at a specific central charge, providing explicit formulas for key correlators.

Contribution

It extends the known non-supersymmetric limit results to the supersymmetric case, including explicit structure constants and boundary states.

Findings

Super Liouville theory at c=3/2 can be obtained as a limit of supersymmetric minimal models.

Explicit three-point functions for bulk fields are derived.

Structure constants are expressed using Barnes' double gamma functions.

Abstract

We show that N=1 supersymmetric Liouville theory can be continued to central charge c=3/2, and that the limiting non-rational superconformal field theory can also be obtained as a limit of supersymmetric minimal models. This generalises a result known for the non-supersymmetric case. We present explicit expressions for the three-point functions of bulk fields, as well as a set of superconformal boundary states. The main technical ingredient to take the limit of minimal models consists in determining analytic expressions for the structure constants. In the appendix we show in detail how the structure constants of supersymmetric and Virasoro minimal models can be rewritten in terms of Barnes' double gamma functions.