On Holomorphic Effective Actions of Hypermultiplets Coupled to External Gauge Superfields

We study the structure of holomorphic effective action for hypermultiplet models interacting with background super Yang-Mills fields. A general form of holomorphic effective action is found for hypermultiplet belonging to arbitrary representation of any semisimple compact Lie group spontaneously broken to its maximal abelian subgroup. The applications of obtained results to hypermultiplets in fundamental and adjoint representations of the SU(n), SO(n), Sp(n) groups are considered.