  The most general four-dimensional non-linear sigma-model, having the
second-order derivatives only and interacting with a background metric and an
antisymmetric tensor field, is constructed. Despite its apparent
non-renormalizability, just imposing the one-loop UV-finiteness conditions
determines the unique model, which may be finite to all orders of the quantum
perturbation theory. This model is known as the four-dimensional
Donaldson-Nair-Schiff theory, which is a four-dimensional analogue of the
standard two-dimensional Wess-Zumino-Novikov-Witten model, and whose unique
finiteness properties and an infinite-dimensional current algebra have long
been suspected.
