N = 2 Super $W_{\infty}$ Algebra and its Nonlinear Realization Through Super KP Formulation

TL;DR

This paper demonstrates a nonlinear realization of the super $W_{}$ algebra via a superLax formulation of the super KP hierarchy, linking it to super KdV hierarchies and their Hamiltonian structures.

Contribution

It introduces a new superLax formulation that realizes the super $W_{}$ algebra nonlinearly and connects it to known super KdV hierarchies.

Findings

SuperLax formulation of super KP hierarchy established.

Reduction yields super KdV hierarchies by Inami and Kanno.

Poisson brackets realize the nonlinear super $W_{}$ algebra.

Abstract

A nonlinear realization of super $W_{\infty}$ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for $N=2$ generalized super KdV hierarchies, proposed by Inami and Kanno. The Lax equations are shown to be Hamiltonian and the associated Poisson bracket algebra among the superfields, consequently, gives rise to a realization of nonlinear super $W_{\infty}$ algebra.