Self-dual gravity as a large- N limit of the 2D non-linear sigma model

The 4D self-dual gravity is shown to be equivalent to a large- N limit of the 2D non-linear sigma model with Wess-Zumino terms only. Infinite dimensional symmetries of the self-dual Einstein equations are derived and shown to form a closed algebra which includes W_∞-a large- N limit of Zamolodchikov's W_N algebra. These are interpreted in terms of Penrose's twistor theory.