D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories

TL;DR

This paper explores the relationship between D-branes on ALE spaces and the ADE classification of conformal field theories, revealing how boundary states encode gauge symmetries and root systems.

Contribution

It establishes a direct physical connection between D-brane spectra on ALE spaces and the ADE classification via boundary states in N=2 superconformal minimal models.

Findings

D2-brane spectra correspond to Lie algebra gauge fields

Boundary states encode ADE root systems

Affine extension includes D0-branes

Abstract

The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of N=2 superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge fields of the corresponding Lie algebra. This provides a simple and direct physical link between the ADE classification of N=2 superconformal field theories, and the corresponding root systems. An affine extension of this structure is also considered, whose boundary states represent the D2-branes plus additional D0-branes.