| Abstract: At finite density, the spontaneous symmetry breaking of an internal non-Abelian symmetry implies not only the existence of gapless modes, but also of gapped ones, whose gap is fixed by the algebra and is proportional to the chemical potential of the system: the gapped Goldstones. The existence of a gap, in turn, raises questions concerning the realization of the symmetry at low energy, as the chemical potential can be as high as the strong coupling scale of the system.
Focussing on the illustrative example of a fully broken SU (2) group, I will show that one can use the coset construction to build a nonrelativistic effective field theory, which realizes nonlinearly Poincaré and the internal symmetry. Remarkably, this effective theory applies also when the strong coupling scale of the system is set by the chemical potential itself, and it includes both gapless and gapped Goldstone modes. To account for the non-conservation of the gapped Goldstone’s number the effective coefficients have imaginary parts, and the resulting theory is thus non-unitary. In this theory gapped Goldstone’s interactions are manifestly controlled by their velocity and power-counting is straightforward. I will conclude with comments on possible applications of this construction |