Self-dual model of SU (2) gauge theory in a space-time with axial symmetry

A model of SU(2) gauge theory with the gauge fields coupled to the scalar fields φ1, φ2 is constructed in terms of local gauge-invariant variables defined over a four-dimensional space-time endowed with axial symmetry. A metric tensor gμν is defined starting with the components Faμν of the strength tensor and its dual F̃aμν. The components gμν are interpreted as new local gauge-invariant variables. Imposing the supplementary condition that the new metric coincides with the initial metric, we obtain the Bogomolny equations for the considered ansatz. The metric gμν assures the property of self-duality for our gauge theory. It is concluded that the self-dual variables are compatible with the axial symmetry of the space-time. An analytical solution of the gauge field equations is also obtained. All the calculations were performed using the GRTensorII computer algebra package, running on the MapleV platform. Finally, we plot the component g00 of the new metric and give this program.