A-D-E Classification of Conformal Field Theories

TL;DR

This paper demonstrates that the ADE classification scheme, well-known in Lie algebra theory, also applies to categorizing families of two-dimensional conformal field theories, revealing a deep mathematical structure.

Contribution

It establishes a novel connection between ADE classification and conformal field theories, extending the scheme's applicability beyond Lie algebras.

Findings

ADE classification describes families of 2D conformal field theories

The scheme reveals underlying algebraic structures in CFTs

Provides a new framework for understanding CFT classifications

Abstract

The ADE classification scheme is encountered in many areas of mathematics, most notably in the study of Lie algebras. Here such a scheme is shown to describe families of two-dimensional conformal field theories.