  We consider non-Abelian 1/2 BPS flux tubes (strings) in a deformed N=2
supersymmetric gauge theory, with mass terms mu_{1,2} of the adjoint fields
breaking N=2 down to N=1. The main feature of the non-Abelian strings is the
occurrence of orientational moduli associated with the possibility of rotations
of their color fluxes inside a global SU(N) group. The bulk four-dimensional
theory has four supercharges; half-criticality of the non-Abelian strings would
imply then N=1 supersymmetry on the world sheet, i.e. two supercharges. In
fact, superalgebra of the reduced moduli space has four supercharges. Internal
dynamics of the orientational moduli are described by two-dimensional CP(N-1)
model on the string world sheet. We focus mainly on the SU(2) case, i.e. CP(1)
world-sheet theory. We show that non-Abelian BPS strings exist for all values
of mu_{1,2}. The low-energy theory of moduli is indeed CP(1), with four
supercharges, in a wide region of breaking parameters mu_{1,2}. Only in the
limit of very large mu_{1,2}, above some critical value, the N=2 world-sheet
supersymmetry breaks down to N=1. We observe "supersymmetry emergence" for the
flux-tube junction (confined monopole): the "kink-monopole" is half-critical
considered from the standpoint of the world-sheet CP(1) model (i.e. two
supercharges conserved), while in the bulk N=1 theory there is no monopole
central charge at all.
