More on gapped Goldstones at finite density: More gapped Goldstones

TL;DR

The paper develops a comprehensive coset-construction framework for spontaneously broken symmetries at finite density, revealing four classes of Goldstone modes: linear gapless, quadratic gapless, fixed-gap, and unfixed-gap. It provides exact counting rules and shows that inverse Higgs constraints act as gauge choices rather than universal constraints, with universal upper and model-dependent lower bounds on unfixed-gap modes. Through explicit SU(2)×U(1) and SO(3) examples, it demonstrates how the spectrum depends on the symmetry-breaking mechanism and representations, and clarifies interpolating fields and energy definitions in finite-density contexts. The work extends to multiple UV realizations to illustrate the model dependence of gaps, and discusses implications for non-relativistic systems, gravity, and potential applications in QCD and cosmology.

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.