Sterile neutrinos and global symmetries

We use an effective-field-theory approach to construct models with naturally light sterile neutrinos, due to either exact or accidental global symmetries. The most attractive models we find are based on gauge symmetries, either discrete or continuous. We give examples of simple models based on ${\mathbf{Z}}_N$, $\mathrm{U}(1{)}^{\prime }$, and $\mathrm{SU}(2{)}^{\prime }$.