# Finite-temperature phase transitions of third and higher order in gauge theories at large $N$

## Abstract

We study phase transitions in *SU*(∞) gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. Here, we speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infnite *N*.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); RIKEN

- OSTI Identifier:
- 1421295

- Alternate Identifier(s):
- OSTI ID: 1434786

- Report Number(s):
- RBRC-1277; BNL-203565-2018-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1802688

- Grant/Contract Number:
- SC0012704

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Nishimura, Hiromichi, Pisarski, Robert D., and Skokov, Vladimir V.
```*Finite-temperature phase transitions of third and higher order in gauge theories at large N*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.036014.

```
Nishimura, Hiromichi, Pisarski, Robert D., & Skokov, Vladimir V.
```*Finite-temperature phase transitions of third and higher order in gauge theories at large N*. United States. doi:10.1103/PhysRevD.97.036014.

```
Nishimura, Hiromichi, Pisarski, Robert D., and Skokov, Vladimir V. Thu .
"Finite-temperature phase transitions of third and higher order in gauge theories at large N". United States.
doi:10.1103/PhysRevD.97.036014.
```

```
@article{osti_1421295,
```

title = {Finite-temperature phase transitions of third and higher order in gauge theories at large N},

author = {Nishimura, Hiromichi and Pisarski, Robert D. and Skokov, Vladimir V.},

abstractNote = {We study phase transitions in SU(∞) gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. Here, we speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infnite N.},

doi = {10.1103/PhysRevD.97.036014},

journal = {Physical Review D},

number = 3,

volume = 97,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2018},

month = {Thu Feb 15 00:00:00 EST 2018}

}