ADE Singularities and Coset Models

TL;DR

This paper explores the relationship between ADE singularities, Landau-Ginzburg models, and superconformal coset models within string theory compactifications, providing exact computations and geometric interpretations.

Contribution

It offers a detailed analysis of ADE models, including exceptional cosets, and connects geometric data of singularities with Landau-Ginzburg fields and potentials.

Findings

Identified perturbations induced by singularity deformations.

Computed Landau-Ginzburg potentials exactly.

Linked Landau-Ginzburg fields to geometric data of singularities.

Abstract

We consider the compactification of the IIA string to (1+1) dimensions on non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the compactification include 4-form fluxes, and a particular class of these models has been argued by Gukov, Vafa and Witten to give rise to a set of perturbed superconformal coset models that also have a Landau-Ginzburg description. We examine all these ADE models in detail, including the exceptional cosets. We identify which perturbations are induced by the deformation of the singularity, and compute the Landau-Ginzburg potentials exactly. We also show how the the Landau-Ginzburg fields and their superpotentials arise from the geometric data of the singularity, and we find that this is most naturally described in terms of non-compact, holomorphic 4-cycles.