More on gapped Goldstones at finite density: More gapped Goldstones

TL;DR

This paper confirms and extends the understanding of gapped and gapless Goldstone modes at finite density, revealing new model-dependent gapped Goldstones and clarifying the role of inverse-Higgs constraints.

Contribution

It provides a coset construction for low-energy effective theories, identifying new gapped Goldstones and analyzing their dependence on symmetry breaking details.

Findings

Confirmed the exact calculability of certain gapped Goldstones.

Discovered additional light gapped Goldstones with model-dependent gaps.

Clarified the interpretation of inverse-Higgs constraints.

Abstract

It was recently argued that certain relativistic theories at finite density can exhibit an unconventional spectrum of Goldstone excitations, with gapped Goldstones whose gap is exactly calculable in terms of the symmetry algebra. We confirm this result as well as previous ones concerning gapless Goldstones for non-relativistic systems via a coset construction of the low-energy effective field theory. Moreover, our analysis unveils additional gapped Goldstones, naturally as light as the others, but this time with a model-dependent gap. Their exact number cannot be inferred solely from the symmetry breaking pattern either, but rather depends on the details of the symmetry breaking mechanism--a statement that we explicitly verify with a number of examples. Along the way we provide what we believe to be a particularly transparent interpretation of the so-called inverse-Higgs constraints for spontaneously broken spacetime symmetries.