# Strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

## Abstract

We study N = 4 super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS / CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single nonzero rotation parameter r 0 which sets a fixed mass scale corresponding to the scalar condensate < O > ~$r$ $$^{4}_{0}$$ in the Coulomb branch. We introduce a new ensemble where T and < O > are held fixed; i.e., the free energy F(T, < O >) is a function of T and < O >. We compute the equation of state (EoS) of N = 4 cSYM at finite T, as well as the heavy quark-antiquark potential and the quantized mass spectrum of the scalar and spin-2 glueballs at T = 0. By computing the Wilson loop (minimal surface) at T = 0, we determine the heavy quark-antiquark potential V(L) to be the Cornell potential, which is confining for large separation L. At T ≠ 0, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with T. We also find a second-order phase transition between the large and small black hole branches with critical temperature T_{c} = T_{min}.

- Authors:

- Publication Date:

- Research Org.:
- Stony Brook Univ., Stony Brook, NY (United States); State Univ. of New York (SUNY), Albany, NY (United States)

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

- OSTI Identifier:
- 1560779

- Alternate Identifier(s):
- OSTI ID: 1610119

- Grant/Contract Number:
- FG02-88ER40388

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; astronomy & astrophysics; physics; field & string theory models & techniques; gauge-gravity dualities; quantum chromodynamics; quark-gluon plasma; relativistic heavy-ion collisions; strings & branes; supergravity

### Citation Formats

```
Mamo, Kiminad A. Strongly coupled N = 4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.066010.
```

```
Mamo, Kiminad A. Strongly coupled N = 4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics. United States. doi:10.1103/PhysRevD.100.066010.
```

```
Mamo, Kiminad A. Mon .
"Strongly coupled N = 4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics". United States. doi:10.1103/PhysRevD.100.066010.
```

```
@article{osti_1560779,
```

title = {Strongly coupled N = 4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics},

author = {Mamo, Kiminad A.},

abstractNote = {We study N = 4 super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS / CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single nonzero rotation parameter r 0 which sets a fixed mass scale corresponding to the scalar condensate < O > ~$r$ $^{4}_{0}$ in the Coulomb branch. We introduce a new ensemble where T and < O > are held fixed; i.e., the free energy F(T, < O >) is a function of T and < O >. We compute the equation of state (EoS) of N = 4 cSYM at finite T, as well as the heavy quark-antiquark potential and the quantized mass spectrum of the scalar and spin-2 glueballs at T = 0. By computing the Wilson loop (minimal surface) at T = 0, we determine the heavy quark-antiquark potential V(L) to be the Cornell potential, which is confining for large separation L. At T ≠ 0, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with T. We also find a second-order phase transition between the large and small black hole branches with critical temperature Tc = Tmin.},

doi = {10.1103/PhysRevD.100.066010},

journal = {Physical Review D},

number = 6,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

DOI: 10.1103/PhysRevD.100.066010

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