Large N field theory of =2 strings and self-dual gravity

We review some aspects of the construction of self-dual gravity and the associated field theory of = 2 strings in terms of two-dimensional sigma models at large N. The theory is defined through a large N Wess—Zumino—Witten model in a nontrivial background and in a particular double scaling limit. We examine the canonical structure of the theory and describe an infinite-dimensional Poisson algebra of currents.