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Advances in High Energy Physics
Volume 2017 (2017), Article ID 6369505, 7 pages
Research Article

Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

1Department of Physics, University of Calcutta, 92 APC Road, Kolkata 700009, India
2Centre for Promotion of Research, 7 Shaktinagar Main Road, Porur, Chennai 600116, India

Correspondence should be addressed to Indrajit Mitra

Received 6 April 2017; Revised 15 June 2017; Accepted 9 July 2017; Published 22 August 2017

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2017 Indrajit Mitra and H. S. Sharatchandra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO() Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.