  A covariant path-integral quantization is proposed for the non-Lagrangian
gauge theory described by the Donaldson-Uhlenbeck-Yau equation. The
corresponding partition function is shown to admit a nice path-integral
representation in terms of the gauged G/G K\"ahler WZW model. A relationship
with the $J$-formulation of the anti-self-dual Yang-Mills theory is explored.
