## Conformal solids and holography

## Abstract

We argue that a SO( *d*) magnetic monopole in an asymptotically AdS space-time is dual to a *d*-dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration *solidon*. In the presence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary — the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.

- Authors:

- Columbia Univ., New York, NY (United States). Dept. of Physics, Center for Theoretical Physics
- Sorbonne Univ., Paris (France)
- Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy, Center for Particle Cosmology

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1506443

- Grant/Contract Number:
- SC0006395; FG02-92ER40699; SC0011941; SC0013528

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; Holography and condensed matter physics (AdS/CMT); Conformal Field Theory; Effective Field Theories; Solitons Monopoles and Instantons

### Citation Formats

```
Esposito, A., Garcia-Saenz, S., Nicolis, A., and Penco, R. Conformal solids and holography. United States: N. p., 2017.
Web. doi:10.1007/jhep12(2017)113.
```

```
Esposito, A., Garcia-Saenz, S., Nicolis, A., & Penco, R. Conformal solids and holography. United States. doi:10.1007/jhep12(2017)113.
```

```
Esposito, A., Garcia-Saenz, S., Nicolis, A., and Penco, R. Wed .
"Conformal solids and holography". United States. doi:10.1007/jhep12(2017)113. https://www.osti.gov/servlets/purl/1506443.
```

```
@article{osti_1506443,
```

title = {Conformal solids and holography},

author = {Esposito, A. and Garcia-Saenz, S. and Nicolis, A. and Penco, R.},

abstractNote = {We argue that a SO(d) magnetic monopole in an asymptotically AdS space-time is dual to a d-dimensional strongly coupled system in a solid state. In light of this, it would be remiss of us not to dub such a field configuration solidon. In the presence of mixed boundary conditions, a solidon spontaneously breaks translations (among many other symmetries) and gives rise to Goldstone excitations on the boundary — the phonons of the solid. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the mixed boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solidon for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find such free energy to be lower than that of thermal AdS. This suggests that our solidon undergoes a solid-to-liquid first order phase transition by melting into a Schwarzschild-AdS black hole as the temperature is raised.},

doi = {10.1007/jhep12(2017)113},

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

number = 12,

volume = 2017,

place = {United States},

year = {2017},

month = {12}

}