Entropy bounds, monotonicity properties and scaling in CFTs

TL;DR

This paper investigates entropy bounds and monotonicity properties in conformal field theories (CFTs), demonstrating bounds for free and strongly coupled CFTs, and revealing thermodynamic parallels with AdS black holes.

Contribution

It establishes entropy bounds in various CFTs, connects these bounds to monotonicity of a generalized C-function, and relates thermodynamics of CFTs with AdS black holes.

Findings

Entropy/energy ratio is bounded in free CFTs but less than Verlinde bound.

Entropy bounds are linked to temperature-dependent monotonicity of a generalized C-function.

Scaling forms of free energy and entropy match AdS black hole thermodynamics.

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 {\cal 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. We show that entropy bounds arise generically in CFTs in connection to monotonicity properties with respect to temperature changes of a generalized C-function. 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. We show that simple scaling forms for the free energy and entropy of CFTs with AdS duals reproduce the thermodynamical properties of (D+1)-dimensional AdS black holes.