Large Nonlinear $W_{\infty}$ Algebras from Nonlinear Integrable Deformations of Self Dual Gravity

TL;DR

This paper constructs a universal nonlinear ${ ilde W}_{inity}$ algebra as a symmetry of deformed self-dual gravity, linking it to integrable systems and quantum gravity applications.

Contribution

It introduces a novel nonlinear algebra derived from deformations of self-dual gravity and explores its quantization, supersymmetrization, and physical relevance.

Findings

Constructed a nonlinear ${ ilde W}_{inity}$ algebra from deformed self-dual gravity.

Linked the algebra to integrable hierarchies like KP and applications in quantum gravity.

Discussed potential for quantization and supersymmetrization of the algebra.

Abstract

A proposal for constructing a universal nonlinear ${\hat W}_{\infty}$ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of $D=4$ Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization and supersymmetrization program can also be carried out. The relevance to the Kadomtsev-Petviashvili hierarchy, $2D$ dilaton gravity, quantum gravity and black hole physics is discussed in the concluding remarks.