Super-bicharacter construction of quantum vertex algebras

TL;DR

This paper generalizes the bicharacter construction of quantum vertex algebras to super Hopf algebras, enabling new quantizations and detailed formulas for field interactions in super vertex algebras.

Contribution

It extends the bicharacter framework to super Hopf algebras and provides explicit formulas for super vertex algebra operations.

Findings

Constructed super vertex algebras via bicharacter methods

Derived formulas for operator product expansion and normal ordering

Enabled different quantizations of super vertex algebras

Abstract

We extend the bicharacter construction of quantum vertex algebras first proposed by Borcherds to the case of super Hopf algebras. We give a bicharacter description of the charged free fermion super vertex algebra, which allows us to construct different quantizations of it in the sense of $H_D$-quantum vertex algebras, or specializations to Etingof-Kazhdan quantum vertex algebras. We give formulas for the analytic continuation of product of fields, the operator product expansion and the normal ordered product in terms of the super-bicharacters.