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

Understand

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.