Exceptional Superconformal Algebras

TL;DR

This paper classifies certain reductive W-algebras generated by specific fields, discovering three new superconformal algebras, including exceptional cases linked to exceptional Lie superalgebras and their quantum versions.

Contribution

It introduces three novel superconformal algebras, including an N=7, N=8, and a symplectic family, expanding the understanding of exceptional superconformal structures.

Findings

Three new superconformal algebras identified

Exceptional cases linked to Lie superalgebras G(3) and F(4)

Quantum versions explicitly constructed

Abstract

Reductive W-algebras which are generated by bosonic fields of spin-1, a single spin-2 field and fermionic fields of spin-3/2 are classified. Three new cases are found: a `symplectic' family of superconformal algebras which are extended by $su(2)\oplus sp(n)$, an $N=7$ and an $N=8$ superconformal algebra. The exceptional cases can be viewed as arising a Drinfeld-Sokolov type reduction of the exceptional Lie superalgebras $G(3)$ and $F(4)$, and have an octonionic description. The quantum versions of the superconformal algebras are constructed explicitly in all three cases.