Logarithmic conformal field theory, log-modular tensor categories and modular forms

Abstract

The two pillars of rational conformal field theory and rational vertex operator algebras are modularity of characters, and the interpretation of its category of modules as a modular tensor category. Overarching these pillars is the Verlinde formula. In this paper we consider the more general class of logarithmic conformal field theories and C2-cofinite vertex operator algebras. We suggest logarithmic variants of those pillars and of Verlinde’s formula. We illustrate our ideas with the -triplet algebras and the symplectic fermions.