  Hidden spin-density waves (hSDW) with Neel ordering vector (pi,pi) have been
proposed recently as parent groundstates to electron-doped iron-selenide
superconductors. Doping such groundstates can result in visible electron-type
Fermi surface pockets and faint hole-type Fermi surface pockets at the corner
of the folded Brillouin zone. A Cooper pair instability that alternates in sign
between the electron-type and the hole-type Fermi surfaces has recently been
predicted. The previous is due to the interaction of electrons and holes with
hidden spin fluctuations connected with hSDW order that is near a
quantum-critical point. Quantum criticality is tuned in by increasing the
strength of Hund's Rule from the hSDW state. We find that the exchange of
hidden spin fluctuations by electrons/holes in the critical hSDW state results
in asymptotic freedom. In particular, the strength of spin-flip interactions
becomes weaker and weaker on length scales that are shorter and shorter
compared to the range of hSDW order. We then argue that string states that
connect well-separated particle/hole excitations in the hSDW are robust. This
suggests a picture where the hole degrees of freedom mentioned previously are
confined.
