  We study the fate of U(1) strings embedded in a non-Abelian gauge theory with
a hierarchical pattern of the symmetry breaking: G->U(1) at V->nothing at v,
V>>v. While in the low-energy limit the Abrikosov-Nielsen-Olesen string (flux
tube) is perfectly stable, being considered in the full theory it is
metastable. We consider the simplest example: the magnetic flux tubes in the
SU(2) gauge theory with adjoint and fundamental scalars. First, the adjoint
scalar develops a vacuum expectation value V breaking SU(2) down to U(1). Then,
at a much lower scale, the fundamental scalar (quark) develops a vacuum
expectation value v creating the Abrikosov-Nielsen-Olesen string. (We also
consider an alternative scenario in which the second breaking, U(1)->nothing,
is due to an adjoint field.) We suggest an illustrative ansatz describing an
"unwinding" in SU(2) of the winding inherent to the Abrikosov-Nielsen-Olesen
strings in U(1). This ansatz determines an effective 2D theory for the unstable
mode on the string world-sheet. We calculate the decay rate (per unit length of
the string) in this ansatz and then derive a general formula. The decay rate is
exponentially suppressed. The suppressing exponent is proportional to the ratio
of the monopole mass squared to the string tension, which is quite natural in
view of the string breaking through the monopole-antimonopole pair production.
We compare our result with the one given by Schwinger's formula dualized for
describing the monopole-antimonopole pair production in the magnetic field.
