Quantum N=2 super $W_3^{(2)}$ Algebra In Superspace

TL;DR

This paper explores the quantum extension of the N=2 supersymmetric $W_3^{(2)}$ algebra in superspace, detailing its structure, constraints, and classical limit at infinite central charge.

Contribution

It introduces the quantum N=2 $W_3^{(2)}$ algebra with generic central charge in superspace, including supercurrents and nonlinear chiral constraints, extending previous classical formulations.

Findings

Quantum N=2 $W_3^{(2)}$ algebra formulated in superspace.

Algebra includes supercurrents with specific spins and constraints.

Classical algebra recovered at infinite central charge.

Abstract

We discuss the N=2 extension of Polyakov-Bershadsky $W_3^{(2)}$ algebra with the generic central charge, $c$, at the quantum level in superspace. It contains, in addition to the spin 1 N=2 stress tensor, the spins $1/2, 2$ bosonic and spins $1/2, 2$ fermionic supercurrents satisfying the first class nonlinear chiral constraints. In the $c \to \infty $ limit, the ``classical'' N=2 $W_3^{(2)}$ algebra is recovered.