Free Field Realization of $N=2$ Super $W_{3}$ Algebra

Abstract

We study the quantum $N=2$ super-$W_{3}$ algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra $A(2|1)$. We compute the full operator product expansions of the algebra explicitly. It is found that the results agree with those obtained by the OPE method.