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

Abstract

A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the 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.

arXiv comment43 pages, subtitle added, new simpler regularization used, sections rewritten to reflect this, conclusions unchanged, version to be published

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• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis II. The measure for gauge fields and a 4d WZW theory