On the Super Field Realization of Super Casimir Wa(n)-Algebras

TL;DR

This paper constructs an explicit quantum super field realization of N=2 super Casimir WA(n)-algebras using supersymmetric Miura transformation, extending the algebra with a super vertex operator based on the Lie superalgebra A(n,n-1).

Contribution

It provides a novel explicit quantum super field construction of super Casimir WA(n)-algebras and extends them with super vertex operators related to A(n,n-1).

Findings

Explicit construction of super Casimir WA(n)-algebras

Extension with super vertex operator based on A(n,n-1)

Connection to supersymmetric Miura transformation

Abstract

We give an explicit quantum super field construction of the N=2 super Casimir WA(n)-algebras, which is obtained from supersymmetric Miura transformation for the Lie superalgebra A(n,n-1). And also we give an extension of this algebra including a super vertex operator which depends on simple root system of A(n,n-1).