Supergroup - extended super Liouville correspondence

TL;DR

This paper establishes a correspondence between supergroup WZNW models and super Liouville theories with extended superconformal symmetry, broadening understanding of their interrelations in conformal field theory.

Contribution

It derives a general relation connecting supergroup WZNW models to super Liouville theories with extended superconformal symmetry, including multiple specific examples.

Findings

Established a correspondence between PSU(1,1|2) WZNW and small N=4 super Liouville theories.

Linked OSP(n|2) WZNW models to superconformal theories with SO(n) symmetry.

Provided a comprehensive derivation for various supergroup WZNW models and their superconformal counterparts.

Abstract

We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL(2) x A for some Lie group A. The corresponding conformal field theory is a super Liouville field theory coupled with the WZNW model on A. An example is a correspondence between the PSU(1,1|2) WZNW model and small N=4 super Liouville field theory. The OSP(n|2) WZNW model is related to a superconformal field theory with SO(n) extended superconformal symmetry of the Knizhnik-Bershadsky type. In the case n=4 this is simply the large N=(4,4) superconformal symmetry. Besides these two examples we make a general derivation encompassing the WZNW models on supergroups SL(2|n), D(2,1;\alpha), OSP(4|2n), F(4) and G(3) and their relation to models with extended superconformal algebras as symmetry.