Lie algebra automorphisms in conformal field theory

TL;DR

This paper explores how automorphisms of infinite-dimensional Lie algebras influence conformal field theory, focusing on symmetry modifications and their implications for boundary conditions and mathematical structures.

Contribution

It introduces new conjectures on the sub-bundle structure of chiral blocks and highlights the significance of Lie algebra automorphisms in conformal field theory.

Findings

Automorphisms lead to symmetry enhancement and reduction.

Conjectures on sub-bundle structures of chiral blocks.

Automorphisms are key in studying boundary conditions.

Abstract

The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures one encounters also appear in other areas of physics and mathematics. In particular, they lead to two conjectures on the sub-bundle structure of chiral blocks, and they are instrumental in the study of conformally invariant boundary conditions.