Yang-Mills theory for semidirect products G ⋉ g* and its instantons

Abstract

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