D-branes, Quivers, and ALE Instantons

TL;DR

This paper explores the gauge theories of D-branes at orbifold points in string theory, linking quiver diagrams to ALE instantons and their moduli spaces, with explicit computations matching known mathematical results.

Contribution

It provides a detailed description of the gauge theories for D-branes on ALE spaces, connecting quiver diagrams with instanton moduli spaces and reproducing known mathematical results.

Findings

Explicit construction of moduli spaces of ALE instantons.

Reproduction of Kronheimer and Nakajima's results for U(N) instantons.

Connection between twisted sector moduli and Fayet-Iliopoulos terms.

Abstract

Effective field theories in type I and II superstring theories for D-branes located at points in the orbifold C^2/Z_n are supersymmetric gauge theories whose field content is conveniently summarized by a `quiver diagram,' and whose Lagrangian includes non-metric couplings to the orbifold moduli: in particular, twisted sector moduli couple as Fayet-Iliopoulos terms in the gauge theory. These theories describe D-branes on resolved ALE spaces. Their spaces of vacua are moduli spaces of smooth ALE metrics and Yang-Mills instantons, whose metrics are explicitly computable. For U(N) instantons, the construction exactly reproduces results of Kronheimer and Nakajima.