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Entropy 2016, 18(5), 169;

Pressure and Compressibility of Conformal Field Theories from the AdS/CFT Correspondence

Department of Mathematical Physics, Maynooth University, Maynooth, Ireland
Dublin Institute for Advanced Studies, 10 Burlington Rd, Dublin D04 C932, Ireland
Academic Editor: David Kubiznak
Received: 16 March 2016 / Revised: 21 April 2016 / Accepted: 22 April 2016 / Published: 3 May 2016
(This article belongs to the Special Issue Black Hole Thermodynamics II)
Full-Text   |   PDF [315 KB, uploaded 3 May 2016]   |  


The equation of state associated with N = 4 supersymmetric Yang–Mills in four dimensions, for S U ( 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 of the quark-gluon plasma 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 three- and six-dimensional conformal field theories again yields mean field exponents associated with the compressibility at the critical point. View Full-Text
Keywords: black hole entropy; thermodynamic phase transitions; AdS/CFT; PV criticality black hole entropy; thermodynamic phase transitions; AdS/CFT; PV criticality

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Dolan, B.P. Pressure and Compressibility of Conformal Field Theories from the AdS/CFT Correspondence. Entropy 2016, 18, 169.

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