Vafa-Witten theorem, vector meson condensates and magnetic-field-induced   electromagnetic superconductivity of vacuum
  We show that the electromagnetic superconductivity of vacuum in strong magnetic field background is consistent with the Vafa-Witten theorem because the charged vector meson condensates lock relevant internal global symmetries of QCD with the electromagnetic gauge group. 
M. N. Chernodub
hep-ph hep-lat