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

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

1994-09-30

arxiv.org/abs/hep-th/9409197v1

Phys. Lett. B353 (1995) 201

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0370-2693(95)00467-Y

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.

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