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

Abstract

The equation of state associated with $\mathcal{N}=4$ 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.

Feature invited paper for special edition "Black hole thermodynamics II" in Entropy, 19 pages, 2 figures. Minor typos corrected in v2

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Holographic Black Hole Chemistry
• Bose condensation and branes
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions

Cited by in corpus (28)

• Black hole chemistry: thermodynamics with Lambda
• Thermodynamics of AdS Black Holes: Central Charge Criticality
• Black holes in Einsteinian cubic gravity
• Holographic CFT Phase Transitions and Criticality for Charged AdS Black Holes
• Holographic heat engines: general considerations and rotating black holes
• Thermodynamics of Gauss-Bonnet-de Sitter Black Holes
• Hairy black holes in cubic quasi-topological gravity
• Restricted thermodynamic fluctuations and the Ruppeiner geometry of black holes
• Black hole chemistry and holography in generalized quasi-topological gravity
• On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography
• Black Hole Chemistry: the first 15 years
• Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity
• Exploring the Phase Transition in Charged Gauss-Bonnet Black Holes: A Holographic Thermodynamics Perspectives
• Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality
• Holographical aspects of dyonic black holes: Massive gravity generalization
• Breaking of universal nature of central charge criticality in $AdS$ black holes in Gauss-Bonnet Gravity
• Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism
• Thermodynamics and phase transition in central charge criticality of charged Gauss-Bonnet AdS black holes
• The shared universality of charged black holes and the many many-body SYK model
• Restricted phase space thermodynamics of Einstein-power-Yang-Mills AdS black hole
• Matching partition functions of deformed JT gravity and the cSYK model
• Thermodynamic geometry of pure Lovelock black holes
• Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory
• Bulk-Boundary Thermodynamics of Charged Black Holes in Higher Derivative Theory
• Statistical ensembles and logarithmic corrections to black hole entropy
• Thermodynamics of Barrow Einstein-power-Yang-Mills AdS black hole in the restricted phase space
• Phase transition structure and breaking of universal nature of central charge criticality in a Born-Infeld $AdS$ black hole
• Noether Charge, Thermodynamics and Phase Transition of a Black Hole in the Schwarzschild-Anti-de Sitter-Beltrami spacetime