On black hole thermodynamics from super Yang-Mills

TL;DR

This paper investigates the thermodynamics of maximally supersymmetric Yang-Mills theories in low dimensions, explaining the temperature dependence of physical quantities via the strong coupling of low-energy moduli, and predicts properties of dual black holes.

Contribution

It provides a theoretical explanation for the peculiar temperature powers in supergravity predictions and extends the analysis to deformed theories like BMN quantum mechanics.

Findings

Derived the origin of temperature powers in supergravity predictions.

Predicted thermodynamic behavior of black holes dual to deformed theories.

Linked low-energy moduli coupling to temperature scaling.

Abstract

We consider maximally supersymmetric U(N) Yang-Mills in (1+p)-dimensions for p < 3. In the 't Hooft large N limit this is conjectured to be dual to N Dp-branes in the decoupling limit. At low temperatures T << \lambda^{1/(3-p)} governed by the dimensionful 't Hooft coupling \lambda, supergravity black holes predict the free energy density goes as ~ N^2 T^{2(7-p)/(5-p)} and the expectation value of the scalars goes as ~ T^{2/(5-p)}, with dimensions made up by \lambda. The purpose of this work is to explain the origin of these peculiar powers of temperature. We argue that these powers naturally arise by requiring that the low energy moduli of the theory become strongly coupled at low temperature. As an application, we consider the BMN quantum mechanics that results from a supersymmetric deformation of the p=0 theory. The black holes dual to this deformed theory have not yet been constructed, and our analysis can be used to make an explicit prediction for their thermodynamic behaviour.