Quantization of Donaldson-Uhlenbeck-Yau theory

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.