Vertex operator superalgebra/sigma model correspondences: The four-torus case

TL;DR

This paper establishes a new correspondence between vertex operator superalgebras and sigma models, specifically demonstrating this for N=(4,4) models on four-tori and comparing it to K3 surfaces, revealing symmetry-based relations.

Contribution

It introduces a novel correspondence framework linking vertex operator superalgebras and sigma models, exemplified on four-tori, expanding understanding beyond previous K3 surface studies.

Findings

Established correspondence for four-tori sigma models

Compared four-tori case with K3 surface case

Highlighted symmetry and reflection properties in the correspondence

Abstract

We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is motivated by previous work on N=(4,4) supersymmetric non-linear sigma models on K3 surfaces and on a vertex operator superalgebra with Conway group symmetry. Here we present an example of the correspondence for N=(4,4) supersymmetric non-linear sigma models on four-tori, and compare it to the K3 case.