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.
Categories: hep-th