On the phase transition of conformal field theories with holographic duals

We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter–Schwarzschild bulk spacetimes. A Cardy–Verlinde formula is derived thermodynamically for CFTs living on Sn×R with Sn having an arbitrary radius. The Hawking–Page phase transition of the CFT is described using Landauʹs theory of phase transitions, and an alternative derivation of the Cardy–Verlinde formula is presented. The condensate in the high temperature phase is identified as being composed of radiational matter.