SUSY Lattice Vertex Algebras

TL;DR

This paper constructs and analyzes supersymmetric lattice vertex algebras, illustrating their structure with a specific example related to a vertex algebra of central charge 3/2.

Contribution

It introduces the construction of SUSY lattice vertex algebras and provides a concrete example linked to a known vertex algebra with central charge 3/2.

Findings

Constructed SUSY lattice vertex algebras from integer lattices.

Identified the simple vertex algebra associated with a specific SUSY lattice.

Connected the SUSY lattice vertex algebra to a known vertex algebra of central charge 3/2.

Abstract

We construct and study SUSY lattice vertex algebras. As a simple example, we obtain the simple vertex algebra associated to the vertex algebra $V_c(N3)$ of central charge $c=3/2$, as the SUSY lattice vertex algebra associated to $\mathbb{Z}$ with bilinear form $(a,b) = 2ab$.