N=2 Superconformal Symmetry in Super Coset Models

TL;DR

This paper extends the Kazama-Suzuki construction to supergroup cosets, identifying new N=2 superconformal models, exemplified by the GL(1|1) WZNW model, revealing intricate supersymmetry structures.

Contribution

It generalizes the Kazama-Suzuki construction to supergroup cosets, providing explicit models with N=2 superconformal symmetry, including the analysis of the GL(1|1) case.

Findings

Constructed N=2 superconformal algebra for GL(1|1) WZNW model

Identified the (anti-)chiral ring structure of the model

Revealed interplay between world-sheet and target space supersymmetry

Abstract

We extend the Kazama-Suzuki construction of models with N=(2,2) world-sheet supersymmetry to cosets S/K of supergroups. Among the admissible target spaces that allow for an extension to N=2 superconformal algebras are some simple Lie supergroups, including PSL(N|N). Our general analysis is illustrated at the example of the N=1 WZNW model on GL(1|1). After constructing its N=2 superconformal algebra we determine the (anti-)chiral ring of the theory. It exhibits an interesting interplay between world-sheet and target space supersymmetry.