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Entropy 2016, 18(5), 169; doi:10.3390/e18050169

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

1
Department of Mathematical Physics, Maynooth University, Maynooth, Ireland
2
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)
View Full-Text   |   Download PDF [315 KB, uploaded 3 May 2016]   |  

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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