Lectures on D-branes, Gauge Theory and M(atrices)
Washington Taylor
TL;DR
The notes present a cohesive program: derive D-brane physics from the low-energy Yang–Mills description of coincident branes, explore how T- and S-duality emerge in this framework, and show how higher-dimensional branes and bound states arise from gauge-theoretic constructions. They then articulate the BFSS Matrix theory conjecture, arguing that the large-N limit of 0-brane matrix quantum mechanics encapsulates M-theory in the infinite-momentum frame, with compactifications yielding supersymmetric Yang–Mills on dual tori and reproducing leading supergravity interactions. The text surveys matrix objects (gravitons, membranes, 5-branes) and their interactions, and discusses Matrix string theory, higher-dimensional compactifications, and the open debates on proofs and limits of the conjecture. The overall message is that super Yang-Mills theory is a powerful, information-rich language for D-branes and M-theory, capable of encoding dualities, bound states, and gravitational dynamics, while also suggesting directions toward noncommutative geometry and more fundamental underpinnings. The work underscores the deep connections between gauge theory, string theory, and quantum gravity, while noting unresolved conceptual and technical challenges in achieving a complete nonperturbative formulation.
Abstract
These notes give a pedagogical introduction to D-branes and Matrix theory. The development of the material is based on super Yang-Mills theory, which is the low-energy field theory describing multiple D-branes. The main goal of these notes is to describe physical properties of D-branes in the language of Yang-Mills theory, without recourse to string theory methods. This approach is motivated by the philosophy of Matrix theory, which asserts that all the physics of light-front M-theory can be described by an appropriate super Yang-Mills theory.