# Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory

## TL;DR

This paper explores the connection between self-dual vertex operator superalgebras and superconformal field theories, providing classification results and examples related to sigma models on tori and K3 surfaces.

## Contribution

It offers a classification of self-dual vertex operator superalgebras with central charge up to 12 and links them to superconformal field theories.

## Key findings

- Classification of self-dual vertex operator superalgebras up to central charge 12
- Examples linking these algebras to sigma models on tori and K3 surfaces
- Insights into the structure of superconformal field theories

## Abstract

Recent work has related the equivariant elliptic genera of sigma models with K3 surface target to a vertex operator superalgebra that realizes moonshine for Conway's group. Motivated by this we consider conditions under which a self-dual vertex operator superalgebra may be identified with the bulk Hilbert space of a superconformal field theory. After presenting a classification result for self-dual vertex operator superalgebras with central charge up to 12 we describe several examples of close relationships with bulk superconformal field theories, including those arising from sigma models for tori and K3 surfaces.