Yang--Mills Configurations from 3D Riemann--Cartan Geometry

Recently, the {\it spacelike} part of the $SU(2)$ Yang–Mills equations has been identified with geometrical objects of a three–dimensional space of constant Riemann–Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza–Klein") {\it mapping} by employing a $(3+1)$–decomposition of {\it Clifford algebra}–valued torsion and curvature two–forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\it Chern–Simons term} plus cosmological term and is therefore of purely topological origin.