On holomorphic effective actions of hypermultiplets coupled to external gauge superfields

We study the structure of holomorphic effective action generated by hypermu ltiplet models interacting with background super-Yang-Mills fields. A gener al form of holomorphic effective action depending on background fields is f ound for hypermultiplet belonging to arbitrary representation of any semisi mple compact Lie group spontaneously broken to its maximal Abelian subgroup . Resulting effective action is defined by the superfield strengths lying i n Cartan subalgebra of the gauge algebra. The applications of the obtained results to hypermultiplets in fundamental and adjoint representations of th e SU(n), SO(n), Sp(n) groups are considered.