Thermodynamics of conformal field theories and cosmology

TL;DR

This paper investigates the entropy-to-energy ratio in conformal field theories at finite temperature, comparing free and strongly coupled cases, and explores bounds and thermodynamic similarities with two-dimensional CFTs.

Contribution

It provides bounds for the entropy-energy ratio in free and strongly coupled CFTs and reveals thermodynamic resemblances with two-dimensional CFTs.

Findings

The ratio is bounded from above in free field realizations.

Strongly coupled CFTs with AdS duals obey the Verlinde bound even with rotation.

Thermodynamic formulas of certain CFTs resemble those of two-dimensional CFTs.

Abstract

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of N=4 super Yang-Mills theory in D=4 and the (2,0) tensor multiplet in D=6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. For strongly coupled CFTs with AdS duals, we show that the ratio obeys the Verlinde bound even in the presence of rotation. For such CFTs, we point out an intriguing resemblance in their thermodynamic formulas with the corresponding ones of two-dimensional CFTs. The discussion is based on hep-th/0101076.