Symmetry Realization via a Dynamical Inverse Higgs Mechanism

Abstract

The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. This phenomena is called an Inverse Higgs Mechanism (IHM). However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We have present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizaing the results for Vishwanath and Wantanabe.

Added a new result for the beta function for the UV theory of unitary fermions

References in corpus (6)

• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
• (Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry
• Nonlinear realizations of symmetries and unphysical Goldstone bosons
• Spontaneous Breaking of Non-Relativistic Scale Symmetry

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• Nonrelativistic Conformal Field Theories in the Large Charge Sector
• The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals
• Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Geometry of Multi-Flavor Galileon-Like Theories
• Gauged Galileons
• Superfluids, vortices and spinning charged operators in 4d CFT
• First Principles Prediction of the Landau Parameter for Fermi Liquids near the Unitarity Limit
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• Fractonic Coset Construction for Spontaneously Broken Translations
• The coset construction for particles of arbitrary spin