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

TL;DR

This paper constructs and analyzes the quantum N=2 super W_3 algebra using free field realization derived from supersymmetric Miura transformation, explicitly computing operator product expansions and confirming their consistency.

Contribution

It provides a new free field realization of the quantum N=2 super W_3 algebra based on the Lie superalgebra A(2|1), with explicit OPE calculations.

Findings

Operator product expansions explicitly computed

Results agree with OPE method calculations

Provides a consistent free field realization

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.