The $N=2$ Super-$W_3^{(2)}$ Algebra

TL;DR

This paper constructs a nonlinear $N=2$ super-$W_3^{(2)}$ algebra with arbitrary central charge, combining superconformal and $W_3^{(2)}$ subalgebras, and explores its realizations and contractions.

Contribution

It introduces a new nonlinear superalgebra structure with explicit construction and realizations, extending the understanding of super-$W$ algebras.

Findings

Constructed the classical nonlinear $N=2$ super-$W_3^{(2)}$ algebra.

Provided hybrid field realization and contraction methods.

Analyzed the algebra's substructure and central charge dependence.

Abstract

We construct the nonlinear $N=2$ super-$W_3^{(2)}$ algebra with an arbitrary central charge at the classical level in the framework of Polyakov "soldering" procedure. It contains two non-intersecting subalgebras: $N=2$ superconformal algebra and $W_3^{(2)}$ and their closure gives the $N=2$ super-$W_3^{(2)}$ algebra. Besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras, it comprises two pairs of fermionic currents with spins 1 and 2. The hybrid field realization and contractions to the zero central charge are constructed.