Staggered modules of $N=2$ superconformal minimal models

TL;DR

This paper explores a special class of indecomposable modules called staggered modules over the $N=2$ superconformal algebra, explicitly constructing examples at specific central charges and analyzing their symmetries and spectral-flow properties.

Contribution

It introduces and constructs explicit examples of staggered modules for $N=2$ superconformal minimal models at $c=-1$ and $c=-6$, advancing understanding of their structure.

Findings

Explicit construction of staggered modules at $c=-1$ and $c=-6

Analysis of spectral-flow orbits and symmetries

Identification of non-diagonalisable $L_0$ action

Abstract

We investigate a class of reducible yet indecomposable modules over the $N=2$ superconformal algebras. These so-called staggered modules exhibit a non-diagonalisable action of the Virasoro mode $L_{0}$. Using recent results on the coset construction of $N=2$ minimal models, we explicitly construct such modules for central charges $c = -1$ and $c = -6$. We also describe spectral-flow orbits and symmetries of the families of staggered modules which arise via the coset.