Supersymmetric extension of universal enveloping vertex algebras

TL;DR

This paper explores the construction of supersymmetric extensions of vertex algebras, demonstrating how universal enveloping SUSY vertex algebras can be extended to higher supersymmetry levels.

Contribution

It introduces a method to extend universal enveloping SUSY vertex algebras from N=n to N=n' supersymmetry levels, advancing the theory of SUSY vertex algebras.

Findings

Universal enveloping SUSY vertex algebras can be extended to higher N' supersymmetry levels.

The construction applies to N=n SUSY Lie conformal algebras.

The extension preserves the algebraic structure of SUSY vertex algebras.

Abstract

In this paper, we study the construction of the supersymmetric extensions of vertex algebras. In particular, for $N = n \in \mathbb{Z}_{+}$, we show the universal enveloping $N = n$ supersymmetric (SUSY) vertex algebra of an $N = n$ SUSY Lie conformal algebra can be extended to an $N = n' > n$ SUSY vertex algebra.