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arXiv · 1307.7614

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

V. P. Nair
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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 K\"ahler-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.

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V. P. Nair. 2013-07-29. On the Gauge-invariant Functional Measure for Gauge Fields on CP^2. https://doi.org/10.1103/physrevd.88.105027

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