TFT construction of RCFT correlators III: Simple currents

TL;DR

This paper uses simple currents to construct and classify symmetric special Frobenius algebras in modular tensor categories, leading to insights into modular invariants, boundary conditions, and conformal defects in RCFT.

Contribution

It introduces a classification of simple current type algebras via abelian group cohomology and connects them to known modular invariants and boundary state formulas.

Findings

Classified simple current algebras using abelian group cohomology

Derived modular invariant torus partition functions

Described boundary conditions and conformal defects in these theories

Abstract

We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hep-th/0007174. Finally, we investigate conformal defects in these theories.