Four - Dimensional AvatarsofTwo - Dimensional

We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising niteness properties and an innnite-dimensional current algebra symmetry. Some correlation functions are determined by this symmetry. One way to deene the theory systematically proceeds by the quantization of moduli spaces of holomorphic vector bundles over algebraic surfaces. We outline how one can deene vertex operators in the theories. Finally , we deene four-dimensional \conformal blocks" and present an analog of the Verlinde formula.