1307.7614 (V. P. Nair)

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

V. P. Nair

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.

View original: http://arxiv.org/abs/1307.7614