  We argue that the world-sheet dynamics of magnetic k-strings in the Higgs
phase of the mass-deformed N=4 theory, is controlled by a bosonic O(3) sigma
model with anisotropy and a topological theta term. The theory interpolates
between a massless O(2) symmetric regime, a massive O(3) symmetric phase and
another massive phase with a spontaneously broken Z_2 symmetry. The first two
phases are separated by a Kosterlitz-Thouless transition. When \theta = \pi the
O(3) symmetric phase flows to an interacting fixed point; sigma model kinks and
their dyonic partners become degenerate, mirroring the behaviour of monopoles
in the parent gauge theory. This leads to the identification of the kinks with
monopoles confined on the string.
