On the Gauge-invariant Functional Measure for Gauge Fields on CP^2

Abstract

We introduce a general parametrization for nonabelian gauge fields on the four-dimensional space ${\mathbb{CP}}^2$. The volume element for the gauge-orbit space or the space of physical configurations is then investigated. The leading divergence in this volume element is obtained in terms of a higher dimensional Wess-Zumino-Witten action, which has previously been studied in the context of Kähler-Chern-Simons theories. This term, it is argued, implies that one needs to introduce a dimensional parameter to specify the integration measure, a step which is a nonperturbative version of the well-known dimensional transmutation in four-dimensional gauge theories.

16 pages, affiliation added, typos corrected

References in corpus (2)

• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• The robustness of the vacuum wave function and other matters for Yang-Mills theory

Cited by in corpus (3)

• Renormalization group analysis of the gluon mass equation
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis II. The measure for gauge fields and a 4d WZW theory
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars