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Pressure and compressibility of conformal field theories from the AdS/CFT correspondence

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arxiv 1603.06279 v2 pith:6Y6G7KND submitted 2016-03-20 hep-th gr-qc

Brian P Dolan This is my paper · ORCID
classification hep-thgr-qc
keywords fieldcompressibilitycriticalassociatedconformalconstantcorrespondencecosmological
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The equation of state associated with ${\cal N}=4$ supersymmetric Yang-Mills in 4 dimensions, for $SU(N)$ in the large $N$ limit, is investigated using the AdS/CFT correspondence. An asymptotically AdS black-hole on the gravity side provides a thermal background for the Yang-Mills theory on the boundary in which the cosmological constant is equivalent to a volume. The thermodynamic variable conjugate to the cosmological constant is a pressure and the $P-V$ diagram is studied. It is known that there is a critical point where the heat capacity diverges and this is reflected in the isothermal compressibility. Critical exponents are derived and found to be mean field in the large $N$ limit. The same analysis applied to 3 and 6 dimensional conformal field theories again yields mean field exponents associated with the compressibility at the critical point.

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Cited by 4 Pith papers

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  1. Finite-cutoff Holographic Thermodynamics

    hep-th 2025-07 conditional novelty 6.0 of 10

    Finite-cutoff holography yields a thermodynamic duality between T^2-deformed CFTs and Schwarzschild-AdS black holes with a Dirichlet wall, including a teardrop coexistence curve with up to three states at one temperature.

  2. Off-shell Thermodynamics and Kinetics of Holographic CFTs Dual to Charged AdS Black Holes

    hep-th 2026-06 unverdicted novelty 4.0 of 10

    The paper computes phase diagrams and first-passage time distributions for phase transitions in three ensembles of holographic CFTs using off-shell free energy and Fokker-Planck kinetics.

  3. Restricted Phase Space Thermodynamics of 4D Dyonic AdS Black Holes: Insights from Kaniadakis Statistics and Emergence of Superfluid $\lambda$-Phase Transition

    hep-th 2024-12 conditional novelty 4.0 of 10

    Using Kaniadakis entropy in restricted phase space thermodynamics, the authors report a superfluid-lambda-like phase transition and an ultra-large unstable black hole branch for 4D dyonic AdS black holes.

  4. Black hole chemistry: thermodynamics with Lambda

    hep-th 2016-08 accept novelty 3.0 of 10

    Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reen...

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