Dreibein as prepotential for three-dimensional Yang-Mills theory (Q1630302)

Summary: We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional \(\mathrm{SO}(3)\) 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.