Superconformal structures of supersymmetric free fermion vertex algebras

TL;DR

This paper introduces a one-parameter deformation of the superconformal vector in supersymmetric free fermion vertex algebras, revealing a shifted N=2 superconformal symmetry using SUSY vertex algebra formalism.

Contribution

It defines the shifted superconformal vector and establishes the corresponding shifted N=2 superconformal symmetry in SUSY charged free fermion vertex algebras, and constructs an N=2 SUSY version of the bc-βγ system.

Findings

Defined the shifted superconformal vector for SUSY free fermion vertex algebras.

Identified the shifted N=2 superconformal symmetry using SUSY vertex algebra formalism.

Constructed an N=2 SUSY bc-βγ system representation.

Abstract

In this paper, we define the shifted superconformal vector of supersymmetric charged free fermion vertex algebras, which is a 1-parameter deformation of the superconformal vector of the SUSY $bc$-$\beta\gamma$ system. Moreover, we find the corresponding shifted $N=2$ superconformal symmetry of SUSY charged free fermion vertex algebras, by using the $N_{K}=1$ SUSY vertex algebra formalism. Finally, in order to describe the shifted $N=2$ superconformal symmetry of the SUSY charged free fermion vertex algebra by $N=2$ superfields, we construct an $N_{K}=2$ SUSY version of the $bc$-$\beta\gamma$ system.