Landau-Ginzburg Description of D-branes on ALE Spaces

TL;DR

This paper uses Landau-Ginzburg mirror theory to analyze D-branes on ALE spaces, providing a simpler alternative to quiver gauge theory and applicable across the entire moduli space.

Contribution

It introduces a Landau-Ginzburg mirror framework for studying D-branes on ALE spaces, simplifying analysis compared to traditional quiver gauge theories.

Findings

Encoded BPS spectrum and marginal stability lines in LG framework

Simpler analysis compared to quiver gauge theory near orbifold point

Applicable to any point on the ALE space moduli space

Abstract

We study the Landau-Ginzburg (LG) mirror theory of the non-linear sigma model on the ALE space ${\cal M}$ obtained by resolving the singularity of the orbifold ${\bf C}^2/{\bf Z}_N$. In the LG description, the data of the BPS spectrum and the lines of marginal stability are encoded in the special Lagrangian submanifolds of the mirror manifold $\hat{{\cal M}}$. Our LG description is quite simple as compared with the quiver gauge theory analysis near the orbifold point. Furthermore our mirror analysis can be applied to any point on the moduli space of ${\cal M}$.