Electroweak axion string and superconductivity
  We study the axion strings with the electroweak gauge flux in the DFSZ axion
model and show that these strings, called the electroweak axion strings, can
exhibit superconductivity without fermionic zero modes. We construct three
types of electroweak axion string solutions. Among them, the string with
$W$-flux can be lightest in some parameter space, which leads to a stable
superconducting cosmic string. We also show that a large electric current can
flow along the string due to the Peccei-Quinn scale much higher than the
electroweak scale. This large current induces a net attractive force between
the axion strings with the same topological charge, which opens a novel
possibility that the axion strings form Y-junctions in the early universe.
