March 19, 1996 | Michael R. Douglas and Gregory Moore
The paper discusses the effective field theories of D-branes located at points in the orbifold \(\mathbb{C}^2/\mathbb{Z}_n\), which are supersymmetric gauge theories with a field content summarized by a 'quiver diagram' and Lagrangian including non-metric couplings to the orbifold moduli. These theories describe D-branes on resolved ALE spaces, and their vacuum spaces are moduli spaces of smooth ALE metrics and Yang-Mills instantons. The construction reproduces results of Kronheimer and Nakajima for \(U(N)\) instantons. The paper also reviews the closed string spectrum and gravitational moduli of ALE spaces, and discusses the massless spectrum of type IIa, type Ib, and type I string theories. It introduces the concept of D-branes on orbifolds and derives the world-volume Lagrangian for D-branes at fixed points, including Chern-Simons couplings and supersymmetric completions. The paper concludes with a comparison of the results with those of Kronheimer and Nakajima, showing that the theories describe a finite region in moduli space.The paper discusses the effective field theories of D-branes located at points in the orbifold \(\mathbb{C}^2/\mathbb{Z}_n\), which are supersymmetric gauge theories with a field content summarized by a 'quiver diagram' and Lagrangian including non-metric couplings to the orbifold moduli. These theories describe D-branes on resolved ALE spaces, and their vacuum spaces are moduli spaces of smooth ALE metrics and Yang-Mills instantons. The construction reproduces results of Kronheimer and Nakajima for \(U(N)\) instantons. The paper also reviews the closed string spectrum and gravitational moduli of ALE spaces, and discusses the massless spectrum of type IIa, type Ib, and type I string theories. It introduces the concept of D-branes on orbifolds and derives the world-volume Lagrangian for D-branes at fixed points, including Chern-Simons couplings and supersymmetric completions. The paper concludes with a comparison of the results with those of Kronheimer and Nakajima, showing that the theories describe a finite region in moduli space.