On the Phase Transition of Conformal Field Theories with Holographic Duals

TL;DR

This paper explores the thermodynamics and phase transitions of conformal field theories with holographic duals, deriving a generalized Cardy-Verlinde formula and analyzing the Hawking-Page transition using Landau's theory.

Contribution

It introduces a thermodynamic derivation of the Cardy-Verlinde formula for CFTs on S^n x R with arbitrary S^n radius and describes the Hawking-Page transition via Landau's theory.

Findings

Derived a generalized Cardy-Verlinde formula for arbitrary S^n radius.

Described the Hawking-Page phase transition using Landau's theory.

Identified the high-temperature condensate as radiational matter.

Abstract

We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter-Schwarzschild bulk space-times. A Cardy-Verlinde formula is derived thermodynamically for CFTs living on S^n x R with S^n having an arbitrary radius. The Hawking-Page phase transition of the CFT is described using Landau's 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.