# On partially massless theory in 3 dimensions

## Abstract

We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. We provide a thorough canonical analysis and identify that whether the theory becomes partially massless depends on the form of the stability condition of the secondary constraint responsible for the absence of the ghost. Generically, it is found to be an equation for a Lagrange multiplier implying that partially massless zwei-dreibein gravity does not exist. However, for special backgrounds this condition is identically satisfied leading to the presence of additional symmetries, which however disappear at quadratic order in perturbations.

- Authors:

- Laboratoire Charles Coulomb UMR 5221, Université Montpellier 2, Place Eugène Bataillon, F-34095, Montpellier (France)
- (France)
- Institut d’Astrophysique de Paris-UMR7095 (GReCO), Université Pierre et Marie Curie and CNRS, 98bis boulevard Arago, F-75014 Paris (France)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22454531

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 03; Other Information: PUBLISHER-ID: JCAP03(2015)043; OAI: oai:repo.scoap3.org:9694; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; EQUATIONS; GAUGE INVARIANCE; GRAVITATION; MATHEMATICAL SPACE; PERTURBATION THEORY; QUANTUM FIELD THEORY; SYMMETRY

### Citation Formats

```
Alexandrov, Sergei, Laboratoire Charles Coulomb UMR 5221, CNRS, Place Eugène Bataillon, F-34095, Montpellier, Deffayet, Cédric, and IHÉS, Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette.
```*On partially massless theory in 3 dimensions*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/03/043.

```
Alexandrov, Sergei, Laboratoire Charles Coulomb UMR 5221, CNRS, Place Eugène Bataillon, F-34095, Montpellier, Deffayet, Cédric, & IHÉS, Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette.
```*On partially massless theory in 3 dimensions*. United States. doi:10.1088/1475-7516/2015/03/043.

```
Alexandrov, Sergei, Laboratoire Charles Coulomb UMR 5221, CNRS, Place Eugène Bataillon, F-34095, Montpellier, Deffayet, Cédric, and IHÉS, Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette. Tue .
"On partially massless theory in 3 dimensions". United States.
doi:10.1088/1475-7516/2015/03/043.
```

```
@article{osti_22454531,
```

title = {On partially massless theory in 3 dimensions},

author = {Alexandrov, Sergei and Laboratoire Charles Coulomb UMR 5221, CNRS, Place Eugène Bataillon, F-34095, Montpellier and Deffayet, Cédric and IHÉS, Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette},

abstractNote = {We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. We provide a thorough canonical analysis and identify that whether the theory becomes partially massless depends on the form of the stability condition of the secondary constraint responsible for the absence of the ghost. Generically, it is found to be an equation for a Lagrange multiplier implying that partially massless zwei-dreibein gravity does not exist. However, for special backgrounds this condition is identically satisfied leading to the presence of additional symmetries, which however disappear at quadratic order in perturbations.},

doi = {10.1088/1475-7516/2015/03/043},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2015,

place = {United States},

year = {Tue Mar 24 00:00:00 EDT 2015},

month = {Tue Mar 24 00:00:00 EDT 2015}

}