Gauge and scalar fields on CP2: A gauge-invariant analysis. I. The effective action from chiral scalars

A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the real two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses and also on relating the WZW action to the instanton liquid picture of QCD.

Automated summary

This article studies the parametrization of gauge fields on complex projective spaces of arbitrary dimension, which is a generalization of the real two-dimensional case. The parametrization allows the gauge transformations to act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. In the case of four dimensions, the nature of the effective action due to the interaction between chiral scalars and gauge fields is considered, and important terms such as a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action are identified.