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

Changhyun Ahn
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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.

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Changhyun Ahn. 1994-10-25. Explicit Construction of $N=2$ $W_3$ Current in the $N=2$ Coset $\frac{SU(3)}{SU(2) \times U(1)}$ Model. https://doi.org/10.1016/0370-2693(95)00144-a

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