Perturbed electroweak strings and fermion zero modes

The effect of perturbations of electroweak strings on quark zero modes is studied in 2+1 and 3+1 dimensions. As first discovered by Naculich, it is found that the bosonic perturbations that destabilize the string give a mass to the zero modes and also lift their degeneracy. The effect of the zero modes on the stability of the string is discussed qualitatively and, based on general arguments, we conjecture that the fermionic vacuum instability found by Naculich should lead to a distortion of the bosonic string but not be responsible for decay.