Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras

TL;DR

This paper classifies all simple smooth modules over the Ramond algebra, a super-Virasoro algebra, and applies these results to classify simple weak twisted modules over certain vertex operator superalgebras.

Contribution

It provides the first complete classification of simple smooth modules over the Ramond algebra, extending the understanding of super-Virasoro algebra representations.

Findings

Simple smooth modules are either highest weight or induced from finite-dimensional modules.

Complete classification of simple smooth modules over the Ramond algebra.

Application to classify simple weak twisted modules over vertex operator superalgebras.

Abstract

Simple smooth modules over the Virasoro algebra and one of the super-Virasoro algebras, named the Neveu-Schwarz algebra, have been classified. This problem remained unsolved for the other super-Virasoro algebra called the Ramond algebra.In this paper, all simple smooth modules over the Ramond algebra are classified. More precisely, we show that a simple smooth module over the Ramond algebra is either a simple highest weight module or isomorphic to an induced module from a simple module over a finite dimensional solvable Lie superalgebra.As an application we obtain all simple weak $\psi$-twisted modules over some vertex operator superalgebras.