Fixed point resolution in conformal field theory

TL;DR

This paper reviews recent advances in fixed point resolution within conformal field theories, focusing on coset models and simple current extensions, highlighting the importance of twining characters and orbit Lie algebras.

Contribution

It provides a comprehensive summary of the mathematical structures involved in fixed point resolution, emphasizing twining characters and orbit Lie algebras.

Findings

Enhanced understanding of fixed point resolution in coset CFTs

Clarification of the role of twining characters and orbit Lie algebras

Insights into non-diagonal modular invariants and simple current extensions

Abstract

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of chiral algebras are investigated. A crucial role is played by the mathematical structures of twining characters and orbit Lie algebras.