Fermionic CFTs at large charge and large N

We study the large-charge sector of large-N fermionic CFTs in three dimensions. Depending on the model and the nature of the fixed charge, we find two types of descriptions: in terms of a superfluid or a Fermi sphere. We explicitly compute the conformal dimensions of the lowest operator of fixed charge and in the superfluid case verify the EFT predictions for the phonon spectrum.