Yang–Mills theory for semidirect products G⋉g∗ and its instantons

Yang–Mills theory with a symmetry algebra that is the semidirect product h⋉h∗ defined by the coadjoint action of a Lie algebra h on its dual h∗ is studied. The gauge group is the semidirect product Gh⋉h∗ , a noncompact group given by the coadjoint action on h∗ of the Lie group Gh of h . For h simple, a method to construct the self–antiself dual instantons of the theory and their gauge nonequivalent deformations is presented. Every Gh⋉h∗ instanton has an embedded Gh instanton with the same instanton charge, in terms of which the construction is realized. As an example, h=su(2) and instanton charge one is considered. The gauge group is in this case SU(2)⋉R3 . Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given