Black holes and the phases of brane thermodynamics

TL;DR

This set of lectures develops brane thermodynamics as a unifying lens for gauge/gravity duality, connecting the dynamics of gauge theories on branes to black-hole thermodynamics through frameworks such as the Horowitz–Polchinski correspondence and AdS/CFT. It emphasizes scaling limits like the Maldacena decoupling limit and the UV/IR relation to delineate when brane-based gauge theories accurately capture gravitational thermodynamics versus when gravitational descriptions dominate, and it situates matrix theory as a low-entropy phase of D$p$-brane dynamics on tori. The discussion proceeds through progressively refined examples, establishing criteria for the validity of different effective descriptions and highlighting the high-entropy phase structure that is largely insensitive to boundary conditions. Overall, the work ties perturbative open-string dynamics, nonperturbative gauge dynamics, and black-hole thermodynamics into a coherent picture of the gauge/gravity duality in maximally supersymmetric settings.

Abstract

Introductory lectures on the relations between the thermodynamics of gauge theory on branes and black holes, including the correspondence principle of Horowitz and Polchinski, the AdS/CFT conjecture, and matrix theory.