Results of the classification of superconformal algebras in two dimensions

TL;DR

This paper completes the classification of superconformal chiral operator product expansion algebras in two dimensions, discovering new exceptional superalgebras and outlining a classification scheme for quasisuperconformal algebras.

Contribution

It introduces new exceptional superconformal algebras, including an N=7 algebra, and provides a classification framework for quasisuperconformal algebras in two dimensions.

Findings

Discovered a novel N=7 superconformal algebra associated with G(3).

Extended known classifications to include a family of superalgebras with affine su2 and usp2N.

Outlined a scheme for classifying quasisuperconformal algebras.

Abstract

A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously known cases and the constructed in our previous paper exceptional $N=8$ superalgebra associated with $F(4)$, a novel exceptional $N=7$ superconformal algebra associated with $G(3)$ is found, as well as a whole family of superalgebras containing affine $\widehat{su}_2 \oplus \widehat{usp}_{2N}$. A classification scheme for quasisuperconformal algebras is also outlined.