Gauge and Scalar Fields on $CP^2$: A Gaugeinvariant Analysis I
Abstract
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the twodimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gaugeinvariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gaugeinvariant mass term and a finite fourdimensional WessZuminoWitten (WZW) action. We comment on relating the mass term to lattice simulations as well as SchwingerDyson analyses, and also on relating the WZW action to the instanton liquid picture of QCD.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.11926
 Bibcode:
 2021arXiv211011926K
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 39 pages