Effective Action of Non-Abelian Monopole-Vortex Complex

We construct effective actions for non-Abelian 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) monopole-vortex complexes in 4d N = 2 supersymmetric gauge theories with gauge groups U(N), U(1) \times SO(2n) and U(1) \times USp(2n). In the color-flavor locked vacuum with degenerate hypermultiplet masses, a subgroup of the color-flavor diagonal symmetry remains unbroken and gives internal orientational moduli to vortices which confine monopoles in the Higgs phase. In this paper we discuss the effective action which describes the interactions between monopoles and the orientational moduli of non-Abelian vortices both from the bulk and vortex worldsheet theories. In the large mass limit, we find that the effective action consists of two-dimensional non-linear sigma models on vortex worldsheets and boundary terms which describes monopole-vortex interactions.