  We consider N=2 supersymmetric QCD with the U(N) gauge group (with no
Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass
term \mu for the adjoint matter, W=\mu A^2, assuming that N\leq N_f<2N. This
deformation breaks N=2 supersymmetry down to N=1. This theory supports
non-Abelian flux tubes (strings) which are stabilized by W. They are referred
to as F-term stabilized strings. We focus on the studies of such strings in the
vacuum in which N squarks condense, at small \mu, so that the Z_N strings
preserve, in a sense, their BPS nature. We calculate string tensions both in
the classical and quantum regimes. Then we translate our results for the
tensions in terms of the effective low-energy weighted CP(N_f-1) model on the
string world sheet. The bulk \mu-deformation makes this theory N= (0,2)
supersymmetric heterotic weighted CP(N_f-1) model in two dimensions. We find
the deformation potential on the world sheet. This significantly expands the
class of the heterotically deformed CP models emerging on the string world
sheet compared to that suggested by Edalati and Tong. Among other things, we
show that nonperturbative quantum effects in the bulk theory are exactly
reproduced by the quantum effects in the world-sheet theory.
