Gapped Goldstones at the cut-off scale: a non-relativistic EFT

Understand

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.