# 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. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. 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 dimensionalmore »

- Authors:

- Carnegie Mellon Univ., Pittsburgh, PA (United States)

- Publication Date:

- Research Org.:
- Univ. of Arizona, Tucson, AZ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1507707

- Grant/Contract Number:
- FG02-04ER41338; FG02-06ER41449

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Space-Time Symmetries; Spontaneous Symmetry Breaking

### Citation Formats

```
Rothstein, Ira Z., and Shrivastava, Prashant.
```*Symmetry realization via a dynamical inverse Higgs mechanism*. United States: N. p., 2018.
Web. doi:10.1007/jhep05(2018)014.

```
Rothstein, Ira Z., & Shrivastava, Prashant.
```*Symmetry realization via a dynamical inverse Higgs mechanism*. United States. doi:10.1007/jhep05(2018)014.

```
Rothstein, Ira Z., and Shrivastava, Prashant. Thu .
"Symmetry realization via a dynamical inverse Higgs mechanism". United States. doi:10.1007/jhep05(2018)014. https://www.osti.gov/servlets/purl/1507707.
```

```
@article{osti_1507707,
```

title = {Symmetry realization via a dynamical inverse Higgs mechanism},

author = {Rothstein, Ira Z. and Shrivastava, Prashant},

abstractNote = {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. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. 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 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), generalizing the results for Vishwanath and Wantanabe.},

doi = {10.1007/jhep05(2018)014},

journal = {Journal of High Energy Physics (Online)},

issn = {1029-8479},

number = 5,

volume = 2018,

place = {United States},

year = {2018},

month = {5}

}