On holomorphic effective actions of hypermultiplets coupled to external gauge superfields

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