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Phase Diagram of N=4 Super-Yang-Mills Theory with R-Symmetry Chemical Potentials
High Energy Physics - Theory · Submitted 7 Feb 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics.
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The abstract, sentence by sentence
The phase diagram of large Nc, weakly-coupled N=4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. In the zero coupling limit, a transition line in the mu-T plane is found, separating a "confined" phase in which the Polyakov loop has vanishing expectation value from a "deconfined" phase in which this order parameter is non-zero. For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc^2). This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. Beyond this point, no long-lived locally stable quasi-equilibrium state exists. The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The phase diagram of large Nc, weakly-coupled N=4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. | contribution 0.93 | 0.77 | 0.05 | asserted 0.89 |
| s1 | In the zero coupling limit, a transition line in the mu-T plane is found, separating a "confined" phase in which the Polyakov loop has vanishing expectation value from a "deconfined" phase in which this order parameter is non-zero. | result 1.00 | 0.87 | 0.17 | asserted 1.00 |
| s2 | For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. | method 0.98 | 0.33 | 0.03 | hedged possibility 1.00 |
| s3 | If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. | result 0.99 | 0.72 | 0.18 | asserted 1.00 |
| s4 | However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc^2). | result 0.99 | 0.81 | 0.13 | asserted 1.00 |
| s5 | This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. | result 0.99 | 0.81 | 0.12 | asserted 1.00 |
| s6 | Beyond this point, no long-lived locally stable quasi-equilibrium state exists. | result 0.98 | 0.75 | 0.12 | asserted 1.00 |
| s7 | The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. | interpretation 0.67 | 0.53 | 0.12 | asserted 0.55 |
| s8 | The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. | interpretation 0.78 | 0.41 | 0.18 | asserted 0.62 |
| s9 | The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known. | interpretation 0.63 | 0.21 | 0.13 | hedged possibility 0.98 |
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The paper
Original abstract
The phase diagram of large Nc, weakly-coupled N=4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. In the zero coupling limit, a transition line in the mu-T plane is found, separating a "confined" phase in which the Polyakov loop has vanishing expectation value from a "deconfined" phase in which this order parameter is non-zero. For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc^2). This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. Beyond this point, no long-lived locally stable quasi-equilibrium state exists. The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known.
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References
How the literature uses it
54 arXiv papers cite this in 111 sentences
Papers citing it · 63 sentences without a confident label
Builds on it 4 papers
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Our analyisis complements the work of [ref] , filling in the low temperature regime of the phase diagram of the theory with chemical potentials.
N=4 SYM on S^3 with Near Critical Chemical Potentials · Introduction · 0.90
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In this section we begin by generalizing the computation of the partition function for free $=4$ SYM on $×S^3$ [ref] to include all five possible chemical potentials.
Decoupling limits of N=4 super Yang-Mills on R x S^3 · Finite temperature behavior in planar limit · 0.98
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This has been subsequently generalised to the case where one has a charge or chemical potential [ref] [ref] (see also [ref] ).
Free Fermions and Thermal AdS/CFT · Eigenvalue Density Analysis at Large $N$ · 0.85
Uses its method or tool 3 papers
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First let us determine the R-charges of the fields using the method in [ref] .
Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories · Spectrum of conserved charges · 1.00
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At zero coupling $g=0$, the full refined partition function [ref] can be computed using Pólya theory [ref] : [equation] where $η_B(T,Ω_i)$ and $η_F(T,Ω_i)$ are the single-particle partition functions for the bosonic and fermionic modes on the three-sphere, computed for $=4$ SYM theory with chemical potentials in Refs. [ref] .
Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations · Zero-coupling limit and single-particle partition functions · 0.84
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Following Ref. [ref] , we define $ϕ_p = 1/√(2) \(X_p + i Y_p\)$, with $X_p$ and $Y_p$ hermitian, which allows us to write our Lagrangian in the form [ref]
On the dispersion of fundamental particles in QCD and N=4 Super Yang-Mills theory · The Lagrangians · 0.92
Compares with it 9 papers
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For R-charged black holes, we can reproduce the phase diagram already obtained in [ref] .
Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories · Phase structure · 0.83
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The picture that we have found above at low temperatures and near the critical chemical potential, nicely complements the results of [ref] .
N=4 SYM on S^3 with Near Critical Chemical Potentials · Metastable plasma at high temperatures · 0.91
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Below we check our tree-level results that emerge from the TBA analysis with the previously derived results of Refs. [ref] using Pólya theory.
Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations · Zero-coupling limit and single-particle partition functions · 1.00
Cites it as support 1 paper
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It is necessary to maintain Gauss' law even at zero coupling to obtain valid results in the limit of the interacting theory as pointed out in [ref] .
Phase Transitions of Charged Kerr-AdS Black Holes from Large-N Gauge Theories · Introduction and summary · 0.98
Cites it as background 21 papers
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To summarize the story thus far, the phase diagram of the free theory was studied in [ref] at all temperatures and chemical potentials.
N=4 SYM on S^3 with Near Critical Chemical Potentials · Low temperatures and a metastable plasma phase · 0.93
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In Refs. [ref] , the phase diagrams in the parameter space of the temperature and the chemical potential are investigated for both sides of the correspondence.
Fragmentation of Spinning Branes · Introduction · 0.89
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Consequently, equilibrium states can be analyzed at temperature $T$ and three chemical potentials $μ_a$, corresponding to the three $U(1)$ factors in $SU(4)$ [ref] .
Instability in ${\cal N}=4$ supersymmetric Yang-Mills theory at finite density · Introduction · 0.89
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