Classification of finite simple Lie conformal superalgebras

TL;DR

This paper provides a comprehensive classification of all finite simple Lie conformal superalgebras and their central extensions, advancing the mathematical understanding of algebraic structures relevant to conformal field theory.

Contribution

It offers the first complete classification of finite simple Lie conformal superalgebras and their central extensions, filling a gap in the mathematical theory.

Findings

Complete classification of finite simple Lie conformal superalgebras

Classification of all their central extensions

Detailed proofs of the classification results

Abstract

The notion of a Lie conformal superalgebra encodes an axiomatic descrption of singular parts of the operator product expansions of chiral fields in conformal field theory. In the paper we give a detailed proof of the classification of all finite simple Lie conformal superalgebras. We also classify all their central extensions.