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

TL;DR

This paper develops a gauge-invariant framework for analyzing gauge and scalar fields on complex projective spaces, focusing on the effective action in four dimensions due to chiral scalars, including mass terms and WZW actions.

Contribution

It generalizes gauge field parametrization to higher-dimensional complex projective spaces and analyzes the effective action for chiral scalars in four dimensions with gauge-invariant terms.

Findings

Identification of a gauge-invariant mass term for gauge fields.

Derivation of a finite four-dimensional WZW action.

Discussion of connections to lattice QCD and instanton models.

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.