  We show that self-ordering scalar fields (SOSF), i.e. non-topological cosmic
defects arising after a global phase transition, cannot explain the B-mode
signal recently announced by BICEP2. We compute the full $C_\ell^{B}$ angular
power spectrum of B-modes due to the vector and tensor perturbations of SOSF,
modeled in the large-N limit of a spontaneous broken global O(N) symmetry. We
conclude that the low-$\ell$ multipoles detected by BICEP2 cannot be due mainly
to SOSF, since they have the wrong spectrum at low multipoles. As a byproduct
we derive the first cosmological constraints on this model, showing that the
BICEP2 B-mode polarization data admits at most a 2-3% contribution from SOSF in
the temperature anisotropies, similar to (but somewhat tighter than) the
recently studied case of cosmic strings.
