Title: 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.