Abstract
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.
Highlights
Introduction and summaryPerhaps counterintuitively, some of the most interesting consequences of symmetries in physics arise when symmetries get broken — spontaneously broken, to be precise
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
These modes are not predicted by a Goldstone theorem, we will refer to them as “Goldstones” since they non-linearly realize some of the broken symmetries, and, in particular, they reduce to standard, gapless Goldstone bosons when the chemical potential is brought to zero
Summary
Some of the most interesting consequences of symmetries in physics arise when symmetries get broken — spontaneously broken, to be precise. Perhaps more interestingly, we find that in general there are other gapped modes, which are not predicted by such a theorem, and whose gaps are not fixed by the symmetry breaking pattern, and yet belong in the low-energy effective field theory These modes are not predicted by a Goldstone theorem, we will refer to them as “Goldstones” since they non-linearly realize some of the broken symmetries, and, in particular, they reduce to standard, gapless Goldstone bosons when the chemical potential is brought to zero. We present the symmetry breaking pattern which will be the starting point of our coset construction: a generic Poincare invariant theory with internal symmetries, broken and unbroken, in a state that has finite density for one internal charge. We discuss an interpretation of the inverse Higgs constraints as a gauge fixing condition
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