Logarithmic CFTs connected with simple Lie algebras

TL;DR

This paper constructs logarithmic conformal field theories linked to semisimple simply-laced Lie algebras and computes their characters using theta functions, advancing understanding of their algebraic structure.

Contribution

It introduces a method to build logarithmic CFTs from root systems of simple Lie algebras and explicitly calculates their characters.

Findings

Characters expressed via theta functions

Logarithmic CFTs connected to Lie algebra root systems

New insights into algebraic structure of these theories

Abstract

For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.