The Cardy-Cartan modular invariant

TL;DR

This paper constructs modular invariant partition functions of charge conjugation type using factorizable Hopf algebras, with coefficients given by the Cartan matrix, relevant for logarithmic conformal field theories.

Contribution

It introduces a method to build modular invariants as characters of coends in categories related to logarithmic CFT using Hopf algebra techniques.

Findings

Partition functions are expressed via the Cartan matrix.

The approach applies to categories similar to those in logarithmic CFT.

Provides a new algebraic framework for modular invariants.

Abstract

Using factorizable Hopf algebras, we construct modular invariant partition functions of charge conjugation, or Cardy, type as characters of coends in categories that share essential features with the ones appearing in logarithmic CFT. The coefficients of such a partition function are given by the Cartan matrix of the theory.