On black hole thermodynamics from super Yang-Mills

Understand

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.