$N=2$ and $N=4$ Subalgebras of Super Vertex Operator Algebras

TL;DR

This paper establishes criteria to identify when $N=2$ or $N=4$ super conformal algebras are subalgebras of super vertex operator algebras, with specific examples and applications to super lattice theories.

Contribution

It provides general criteria for recognizing $N=2$ and $N=4$ super conformal subalgebras within super vertex operator algebras, including super lattice cases.

Findings

Criteria for subalgebra identification

Examples of super conformal subalgebras

Application to super lattice theories

Abstract

We develop criteria to decide if an $N=2$ or $N=4$ super conformal algebra is a subalgebra of a super vertex operator algebra in general, and of a super lattice theory in particular. We give some specific examples.