We introduce a general parametrization for nonabelian gauge fields on the four-dimensional space CP^2. The volume element for the gauge-orbit space or the space of physical configurations is then investigated. The leading divergence in this volume element is obtained in terms of a higher dimensional Wess-Zumino-Witten action, which has previously been studied in the context of Kahler-Chern-Simons theories. This term, it is argued, implies that one needs to introduce a dimensional parameter to specify the integration measure, a step which is a nonperturbative version of the well-known dimensional transmutation in four-dimensional gauge theories.
Nair, V. Parameswaran, "On the Gauge-invariant Functional Measure for Gauge Fields on CP^2" (2013). CUNY Academic Works.