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

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