  At finite density, the spontaneous breakdown of an internal non-Abelian
symmetry dictates, along with gapless modes, modes whose gap is fixed by the
algebra and proportional to the chemical potential: the gapped Goldstones.
Generically the gap of these states is comparable to that of other
non-universal excitations or to the energy scale where the dynamics is strongly
coupled. This makes it non-straightforward to derive a universal ef effective
field theory (EFT) description realizing all the symmetries. Focusing on the
illustrative example of a fully broken SU (2) group, we demonstrate that such
an EFT can be constructed by carving out around the Goldstones, gapless and
gapped, at small 3-momentum. The rules governing the EFT, where the gapless
Goldstones are soft while the gapped ones are slow, are those of standard
nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the
EFT Lagrangian formally preserves gapped Goldstone number, and processes where
such number is not conserved are described inclusively by allowing for
imaginary parts in the Wilson coefficients. Thus, while the symmetry is
manifestly realized in the EFT, unitarity is not. We comment on the application
of our construction to the study of the large charge sector of conformal field
theories with non-Abelian symmetries.

High Energy Physics - Theory;Other Condensed Matter;Strongly Correlated Electrons