Representations of N=2 superconformal vertex algebra

Abstract

Let $L_c$ be simple vertex operator superalgebra(SVOA) associated to the vacuum representation of N=2 superconformal algebra with the central charge $c$. Let $c_m=3m/m+2$. We classify all irreducible modules for the SVOA $L_{c_m}$. When $m$ is an integer we prove that the set of all unitary representations of N=2 superconformal algebra with the central charge $c_m$ provides all irreducible $L_{c_m}$-modules. When $m\notin \mathbb{N}$ and $m$ is an admissible rational number we show that irreducible $L_{c_m}$-modules are parameterized with the union of one finite set and union of finitely many rational curves.

22 pages, Latex