  We study the impact of QCD axion strings in the cosmological history of
electroweak (EW) symmetry breaking, focussing on the minimal KSVZ axion model.
We consider the case of the pure SM Higgs potential as well as a simple
scenario with a first order EW phase transition. We capture the effect of the
Peccei-Quinn (PQ) sector within an effective-theory approach for the Higgs
field, where the axion string core and the heavy PQ states are integrated out.
The relevant parameters in this effective theory are controlled by the size of
the portal coupling between the Higgs and the PQ scalar, and the mass of the PQ
radial excitation. We determine the range of portal couplings for which the
axion strings can strongly affect the dynamics of EW symmetry breaking. In the
case of a first order EW phase transition, the strings can act as seeds by
either catalyzing the nucleation of (non-spherical) bubbles, or leading to the
completion of the phase transition by triggering a classical instability.
