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

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

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

Authors

Garcia-Compean, Hugo

Plebanski, Jerzy F.

Przanowski, Maciej

Description

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.
35 pages, phyzzx file, no figures, some coefficiets of Lagrangians were corrected