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

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.

10, IAEC594 ( May, 1994. Revised, Sept. 94)

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• A Moyal Quantization of the Continuous Toda Field
• Aspects of Higher-Spin Theory with Fermions