The Dirac sea contribution to the energy of an electroweak string

We present a systematic determination of the order h fermionic energy shift when an electroweak string is perturbed. We show that the combined effect of zero-modes, bound states and continuum states is to lower the total ferm ionic ground state energy of the string when the Higgs instability of the s tring is excited. The effect of the Dirac sea is thus to destabilise the st ring. However, this effect can be offset by populating positive energy stat es. Fermions enhance the stability of an electroweak string with sufficient ly populated fermionic bound states. (C) 2000 Elsevier Science B.V. All rig hts reserved.