Spectra of Conformal Field Theories with Current Algebras

TL;DR

This paper reviews recent work on classifying the spectra of 2D rational conformal field theories with current algebra symmetries, focusing on partition functions for theories with simple Lie algebra structures.

Contribution

It provides a complete classification of partition functions for RCFTs with simple Lie algebra current algebras, highlighting underlying concepts and simple illustrative examples.

Findings

Classified all possible partition functions for RCFTs with simple Lie algebra current algebras.

Clarified the underlying concepts of the classification process.

Provided illustrative examples to demonstrate the classification approach.

Abstract

This is an elementary review of our recent work on the classification of the spectra of those two-dimensional rational conformal field theories (RCFTs) whose (maximal) chiral algebras are current algebras. We classified all possible partition functions for such theories when the defining finite-dimensional Lie algebra is simple. The concepts underlying this work are emphasized, and are illustrated using simple examples.