Geometry Associated with Self-dual Yang-Mills and the Chiral Model Approaches to Self-dual Gravity

Hugo Garcia-Compean; Jerzy F. Plebanski; Maciej Przanowski

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arXiv · hep-th/9702046

Geometry Associated with Self-dual Yang-Mills and the Chiral Model Approaches to Self-dual Gravity

Hugo Garcia-Compean·Jerzy F. Plebanski·Maciej Przanowski

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Abstract

A geometric formulation of the Moyal deformation for the Self-dual Yang-Mills theory and the Chiral Model approach to Self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of the six-dimensional version of the second heavenly equation and the Park-Husain heavenly equation. The Wess-Zumino-Witten-like Lagrangian of Self-dual gravity is re-examined within this context.

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Hugo Garcia-Compean, Jerzy F. Plebanski, Maciej Przanowski. 1997-02-11. Geometry Associated with Self-dual Yang-Mills and the Chiral Model Approaches to Self-dual Gravity. https://arxiv.org/abs/hep-th/9702046

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