Z strings in the Weinberg-Salam model including fermions are unstable for all values of the parameters. The cause of this instability is the fermion vacuum energy in the Z-string background. Z strings with nonzero fermion densities, however, may still be stable. © 1995 The American Physical Society.
Naculich, Stephen G., "Fermions destabilize electroweak strings" (1995). Physics Faculty Publications. 155.