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A parametrization of gauge fields on complex projective spaces of arbitrarydimension is given as a generalization of the two-dimensional case. Gaugetransformations act homogeneously on the fields, facilitating a manifestlygauge-invariant analysis. Specializing to four dimensions, we consider thenature of the effective action due to chiral scalars interacting with the gaugefields. The key qualitatively significant terms include a possiblegauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten(WZW) action. We comment on relating the mass term to lattice simulations aswell as Schwinger-Dyson analyses, and also on relating the WZW action to theinstanton liquid picture of QCD.

Gauge and Scalar Fields on $\mathbb{CP}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars