# Anatomy of deconfinement

## Abstract

In the weak coupling limit of $${\rm SU}(N)$$ Yang-Mills theory and the $${\rm O}(N)$$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $$\frac{M}{N}$$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can serve as an alternative definition of the deconfinement transition in theories without center symmetry, such as QCD. We also discuss the role of the color degrees of freedom in the emergence of the bulk geometry in holographic duality.

- Authors:

- Univ. of Southampton (United Kingdom)
- Brown Univ., Providence, RI (United States)
- Brown Univ., Providence, RI (United States); Univ. of California, Davis, CA (United States)
- Univ. of Copenhagen (Denmark). The Niels Bohr Inst.

- Publication Date:

- Research Org.:
- Brown Univ., Providence, RI (United States); Univ. of California, Davis, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1596977

- Grant/Contract Number:
- [SC0010010; SC0019480]

- 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: 2019; 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; Black Holes in String Theory; Gauge-gravity correspondence

### Citation Formats

```
Hanada, Masanori, Jevicki, Antal, Peng, Cheng, and Wintergerst, Nico. Anatomy of deconfinement. United States: N. p., 2019.
Web. doi:10.1007/JHEP12(2019)167.
```

```
Hanada, Masanori, Jevicki, Antal, Peng, Cheng, & Wintergerst, Nico. Anatomy of deconfinement. United States. doi:10.1007/JHEP12(2019)167.
```

```
Hanada, Masanori, Jevicki, Antal, Peng, Cheng, and Wintergerst, Nico. Mon .
"Anatomy of deconfinement". United States. doi:10.1007/JHEP12(2019)167. https://www.osti.gov/servlets/purl/1596977.
```

```
@article{osti_1596977,
```

title = {Anatomy of deconfinement},

author = {Hanada, Masanori and Jevicki, Antal and Peng, Cheng and Wintergerst, Nico},

abstractNote = {In the weak coupling limit of ${\rm SU}(N)$ Yang-Mills theory and the ${\rm O}(N)$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $\frac{M}{N}$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can serve as an alternative definition of the deconfinement transition in theories without center symmetry, such as QCD. We also discuss the role of the color degrees of freedom in the emergence of the bulk geometry in holographic duality.},

doi = {10.1007/JHEP12(2019)167},

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

number = [12],

volume = [2019],

place = {United States},

year = {2019},

month = {12}

}

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