Modular Invariant Representations of the Superconformal Algebra

Abstract

Abstract We compute the modular transformation formula of the characters for a certain family of (finitely or uncountably many) simple modules over the simple $\mathcal{N}=2$ vertex operator superalgebra of central charge $c_{p,p^{\prime }}=3\left (1-\frac{2p^{\prime }}{p}\right ),$ where (p, p′) is a pair of coprime positive integers such that p ≥ 2. When p′ = 1, the formula coincides with that of the $\mathcal{N}=2$ unitary minimal series found by F. Ravanini and S.-K. Yang. In addition, we study the properties of the corresponding “modular S-matrix”, which is no longer a matrix if p′≥ 2.