The Lagrangian of a self-dual gravitational field as a limit of the SDYM Lagrangian

Abstract

The action for the su( N) SDYM equations is shown to give in the limit N → ∞ the action for the six-dimensional version of the second heavenly equation. The symmetry reductions of this latter equation to the well known equations of self-dual gravity are given. The Moyal deformation of the heavenly equations are also considered.