A classical N=4 super W_3 algebra

TL;DR

This paper constructs a classical superextension of the Virasoro algebra, specifically an N=4 super W_3 algebra, using Ward identities and subalgebra structures.

Contribution

It introduces a new N=4 super W_3 algebra by extending the Virasoro algebra with superconformal symmetries using a novel approach.

Findings

Complete form of the N=4 super W_3 algebra provided

Extension from N=2 to N=4 superconformal algebra demonstrated

Method based on Ward identities and subalgebra structure

Abstract

I construct classical superextensions of the Virasoro algebra by employing the Ward identities of a linearly realized subalgebra. For the $N=4$ superconformal algebra, this subalgebra is generated by the $N=2$ $U(1)$ supercurrent and a spin~0 $N=2$ superfield. I show that this structure can be extended to an $N=4$ super $W_3$ algebra, and give the complete form of this algebra.