Fractonic Coset Construction for Spontaneously Broken Translations

TL;DR

This paper develops effective field theories for modes arising from homogeneous breaking of translations and other symmetries, revealing how different methods impact the resulting theories and uncovering fractonic modes with constrained mobility.

Contribution

It introduces a coset construction approach for homogeneous translation breaking, highlighting the effects of inverse Higgs constraints and revealing emergent fractonic modes.

Findings

Different methods yield physically distinct effective theories.

Homogeneous translation breaking causes mixing of internal and spacetime symmetries.

Emergent fractonic modes exhibit constrained mobility.

Abstract

We study the homogeneous breaking of spatial translation symmetry concomitantly with the spontaneous breaking of other internal and spacetime symmetries, including dilations. We use the symmetry-breaking pattern as the only input to derive, via the coset construction, general effective field theories for the symmetry-originated modes associated with Goldstone's theorem, namely the Nambu-Goldstone candidates. Through explicit computations, we show that integrating out the explicit massive Nambu-Goldstone candidates or imposing symmetric constraints, namely the inverse Higgs constraints, to express massive modes in terms of the massless ones leads to physically distinct effective field theories. This sensitivity to the chosen method can be traced back to the homogeneous breaking of translations, the homogeneous aspect of the breaking induces a mixing between internal and spacetime symmetries at the level of the Lie algebra. This, in turn, leads to subtle discussions about the inverse Higgs constraints, in particular that they lead to a loss of generality in our specific examples. The derived general effective field theories also give rise to a broad class of theories exhibiting emergent enhanced shift symmetries, which constrain the mobility of the modes. The latter are referred to as fractonic modes.