# 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., 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. https://doi.org/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. https://doi.org/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}

}

https://doi.org/10.1103/PhysRevD.100.066010

*Citation information provided by*

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Web of Science

#### Figures / Tables:

Works referenced in this record:

##
Anti-de Sitter space, thermal phase transition, and confinement in gauge theories

journal, January 1998

- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3

##
Holographic entanglement entropy and thermodynamic instability of planar $R$ -charged black holes

journal, September 2014

- Wu, Xing
- Physical Review D, Vol. 90, Issue 6

##
Chiral phase transition in the soft-wall model of AdS/QCD

journal, April 2016

- Chelabi, Kaddour; Fang, Zhen; Huang, Mei
- Journal of High Energy Physics, Vol. 2016, Issue 4

##
Thermodynamic stability and phases of general spinning branes

journal, July 1999

- Cvetic, Mirjam; Gubser, Steven S.
- Journal of High Energy Physics, Vol. 1999, Issue 07

##
Wilson Loops in Large $\mathit{N}$ Field Theories

journal, June 1998

- Maldacena, Juan
- Physical Review Letters, Vol. 80, Issue 22

##
Low Energy Hadron Physics in Holographic QCD

journal, April 2005

- Sakai, T.; Sugimoto, S.
- Progress of Theoretical Physics, Vol. 113, Issue 4

##
Dynamic critical phenomena at a holographic critical point

journal, December 2011

- DeWolfe, Oliver; Gubser, Steven S.; Rosen, Christopher
- Physical Review D, Vol. 84, Issue 12

##
Non-extreme black holes of five-dimensional N = 2 AdS supergravity

journal, July 1999

- Behrndt, K.; Cvetič, M.; Sabra, W. A.
- Nuclear Physics B, Vol. 553, Issue 1-2

##
Finite density QCD via an imaginary chemical potential

journal, January 2003

- D’Elia, Massimo; Lombardo, Maria-Paola
- Physical Review D, Vol. 67, Issue 1

##
Towards the Large $\mathit{N}$ Limit of Pure $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\mathrm{}$ Super Yang-Mills Theory

journal, January 2001

- Maldacena, Juan; Nuñez, Carlos
- Physical Review Letters, Vol. 86, Issue 4

##
Critical Behavior in the Rotating D-Branes

journal, September 1999

- Cai, Rong-Gen; Soh, Kwang-Sup
- Modern Physics Letters A, Vol. 14, Issue 27

##
Adding flavor to AdS/CFT

journal, June 2002

- Karch, Andreas; Katz, Emanuel
- Journal of High Energy Physics, Vol. 2002, Issue 06

##
Hydrodynamics of R-charged black holes

journal, March 2006

- Son, Dam T.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2006, Issue 03

##
Strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma on the Coulomb branch. II. Transport coefficients and hard probe parameters

journal, September 2019

- Mamo, Kiminad A.
- Physical Review D, Vol. 100, Issue 6

##
Gauge theory correlators from non-critical string theory

journal, May 1998

- Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
- Physics Letters B, Vol. 428, Issue 1-2

##
Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities

journal, August 2000

- Klebanov, Igor R.; Strassler, Matthew J.
- Journal of High Energy Physics, Vol. 2000, Issue 08

##
Hadronic Spectrum of a Holographic Dual of QCD

journal, May 2005

- de Téramond, Guy F.; Brodsky, Stanley J.
- Physical Review Letters, Vol. 94, Issue 20

##
Supergravity and the jet quenching parameter in the presence of R-charge densities

journal, January 2007

- Avramis, Spyros D.; Sfetsos, Kostandinos
- Journal of High Energy Physics, Vol. 2007, Issue 01

##
Linear confinement and AdS/QCD

journal, July 2006

- Karch, Andreas; Katz, Emanuel; Son, Dam T.
- Physical Review D, Vol. 74, Issue 1

##
The large $N$ limit of superconformal field theories and supergravity

journal, January 1998

- Maldacena, Juan
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2

##
Anti de Sitter space and holography

journal, January 1998

- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2

##
Consistent SO(6) reduction of type IIB supergravity on S

journal, October 2000

- Cvetič, M.; Lü, H.; Pope, C. N.
- Nuclear Physics B, Vol. 586, Issue 1-2

##
Gauge theories with imaginary chemical potential and the phases of QCD

journal, December 1986

- Roberge, André; Weiss, Nathan
- Nuclear Physics B, Vol. 275, Issue 4

##
Energy loss, equilibration, and thermodynamics of a baryon rich strongly coupled quark-gluon plasma

journal, April 2016

- Rougemont, Romulo; Ficnar, Andrej; Finazzo, Stefano I.
- Journal of High Energy Physics, Vol. 2016, Issue 4

##
The QCD phase diagram for small densities from imaginary chemical potential

journal, October 2002

- de Forcrand, Philippe; Philipsen, Owe
- Nuclear Physics B, Vol. 642, Issue 1-2

##
QCD and a Holographic Model of Hadrons

journal, December 2005

- Erlich, Joshua; Katz, Emanuel; Son, Dam T.
- Physical Review Letters, Vol. 95, Issue 26

##
States and curves of five-dimensional gauged supergravity

journal, May 2000

- Bakas, Ioannis; Sfetsos, Konstadinos
- Nuclear Physics B, Vol. 573, Issue 3

##
Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories

journal, September 2000

- Cvetič, M.; Gubser, S. S.; Lü, H.
- Physical Review D, Vol. 62, Issue 8

##
The Witten-Sakai-Sugimoto model: A brief review and some recent results

journal, January 2015

- Rebhan, Anton
- EPJ Web of Conferences, Vol. 95

##
Embedding AdS black holes in ten and eleven dimensions

journal, October 1999

- Cveticˇ, M.; Duff, M. J.; Hoxha, P.
- Nuclear Physics B, Vol. 558, Issue 1-2

##
Glueball mass spectrum from supergravity

journal, January 1999

- Csáki, Csaba; Ooguri, Hirosi; Oz, Yaron
- Journal of High Energy Physics, Vol. 1999, Issue 01

##
The Coulomb branch of gauge theory from rotating branes

journal, March 1999

- Kraus, Per; Larsen, Finn; Trivedi, Sandip P.
- Journal of High Energy Physics, Vol. 1999, Issue 03

##
Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories

journal, January 1999

- Brandhuber, A.; Sfetsos, K.
- Advances in Theoretical and Mathematical Physics, Vol. 3, Issue 4

##
Mesons in gauge/gravity duals

journal, January 2008

- Erdmenger, J.; Evans, N.; Kirsch, I.
- The European Physical Journal A, Vol. 35, Issue 1

##
Robustness and infrared sensitivity of various observables in the application of AdS/CFT to heavy ion collisions

journal, August 2008

- Liu, Hong; Rajagopal, Krishna; Shi, Yeming
- Journal of High Energy Physics, Vol. 2008, Issue 08

##
Bulk viscosity of strongly coupled plasmas with holographic duals

journal, August 2008

- Gubser, Steven S.; Pufu, Silviu S.; Rocha, Fábio D.
- Journal of High Energy Physics, Vol. 2008, Issue 08

##
Holographic Phase Transitions with Fundamental Matter

journal, August 2006

- Mateos, David; Myers, Robert C.; Thomson, Rowan M.
- Physical Review Letters, Vol. 97, Issue 9

##
Thermalization of quark-gluon plasma in magnetic field at strong coupling

journal, November 2015

- Mamo, Kiminad A.; Yee, Ho-Ung
- Physical Review D, Vol. 92, Issue 10

##
Thermodynamics of spinning D3-branes

journal, July 1999

- Gubser, Steven S.
- Nuclear Physics B, Vol. 551, Issue 3

##
Phases of R-charged black holes, spinning branes and strongly coupled gauge theories

journal, April 1999

- Cvetic, Mirjam; Gubser, Steven S.
- Journal of High Energy Physics, Vol. 1999, Issue 04

##
Imaginary chemical potential and finite fermion density on the lattice

journal, January 1999

- Alford, Mark; Kapustin, Anton; Wilczek, Frank
- Physical Review D, Vol. 59, Issue 5

##
Spin-two glueballs, positive energy theorems and the AdS/CFT correspondence

journal, October 1999

- Constable, Neil R.; Myers, Robert C.
- Journal of High Energy Physics, Vol. 1999, Issue 10

##
Adding flavor to AdS/CFT

journal, July 2003

- Karch, A.; Katz, A.
- Fortschritte der Physik, Vol. 51, Issue 78

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*