Explicit Construction of $N=2$ $W_3$ Current in the $N=2$ Coset $\frac{SU(3)}{SU(2) \times U(1)}$ Model

TL;DR

This paper constructs an explicit $N=2$ $W_3$ current within the $SU(3)/SU(2) imes U(1)$ coset model using superspace methods, extending the superconformal algebra and matching known results.

Contribution

It provides a new explicit superspace construction of the $N=2$ $W_3$ algebra for the Kazama-Suzuki coset model, generalizing previous component-based work.

Findings

Successfully reproduces the $N=2$ $W_3$ algebra in superspace formalism.

Generalizes Sugawara and coset constructions for $N=2$ superconformal algebra.

Matches known algebra results for the minimal series at various levels.

Abstract

We discuss the nonlinear extension of $N=2$ superconformal algebra by generalizing Sugawara construction and coset construction built from $N=2$ currents based on Kazama-Suzuki $N=2$ coset model $\frac{SU(3)}{SU(2) \times U(1)}$ in $N=2$ superspace. For the generic unitary minimal series $c = 6(1-\frac{3}{k+3})$ where $k$ is the level of $SU(3)$ supersymmetric Wess-Zumino-Witten model, this algebra reproduces exactly $N=2$ $W_3$ algebra which has been worked out by Romans in component formalism.