The Full Structure of Quantum $N=2$ Super-$W_3^{(2)}$ Algebra

TL;DR

This paper fully describes the quantum structure of an extended N=2 super W3^{(2)} algebra, including additional fermionic currents, and discusses its classical limit and field realization.

Contribution

It provides the complete quantum algebra structure of the N=2 super W3^{(2)} algebra with additional fermionic currents, extending previous classical results.

Findings

Complete quantum algebra structure derived

Additional fermionic currents identified

Classical limit matches previous studies

Abstract

We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with integer spins 1 and 2, besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras. For $c\rightarrow \infty$ limit, the algebra reduces to the classical one, which has been studied previously. The 'hybrid' field realization of this algebra is also discussed.