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

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-twisted modules over some vertex operator superalgebras.