Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian vortices are studied in 4d N = 2 supersymmetric U(1) × SO(2n) and U(1) × USp(2n) gauge theories, with Nf = 2n quark multiplets. The 2d N = (2, 2) effective worldsheet sigma models on the Hermitian symmetric spaces SO(2n)/U(n) and USp(2n)/U(n) found recently which describe the low-energy excitations of the orientational moduli of the vortices, are generalized to the respective massive sigma models. The continuous vortex moduli spaces are replaced by a finite number (2n-1 or 2n) of vortex solutions. The 1/2 BPS kinks connecting different vortex vacua are magnetic monopoles in the 4d theory, trapped inside the vortex core, with total configurations being 1/4 BPS composite states. These configurations are systematically studied within the semi-classical regime.
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