Holographic Black Hole Chemistry

TL;DR

This paper explains how the thermodynamic properties of black holes in Anti-de Sitter space relate to the dual holographic field theory, emphasizing the role of the number of colors in gauge theories.

Contribution

It demonstrates that the generalized Smarr relation for black holes can be understood through the dependence of thermodynamic quantities on the number of colors in the dual gauge theory.

Findings

Thermodynamic quantities scale with N^2 in large N gauge theories.

The generalized Smarr relation reflects the dependence of extensive quantities on N.

Holographic interpretation clarifies black hole thermodynamics in AdS space.

Abstract

Thermodynamic quantities associated with black holes in Anti-de Sitter space obey an interesting identity when the cosmological constant is included as one of the dynamical variables, the generalized Smarr relation. We show that this relation can easily be understood from the point of view of the dual holographic field theory. It amounts to the simple statement that the extensive thermodynamic quantities of a large $N$ gauge theory only depend on the number of colors, $N$, via an overall factor of $N^2$.