Explicit construction of N = 2 W3 current in the N = 2 coset SU(3)SU(2)×U(1) model

We discuss the nonlinear extension of N = 2 superconformal algebra by generalizing Sugawara construction and coset construction built from N = 2 current algebra based on Kazama-Suzuki N = 2 coset model SU(3)SU(2)×U(1) in N = 2 superspace. For the generic unitary minimal series c = 6(1 − 3k+3) where k is the leve of SU(3) supersymmetric Wess-Zumino-Witten model, this algebra reproduces exactly N = 2 W3 algebra which has been worked out by Romans in component formalism.