Landau-Ginzburg skeletons

Abstract

We study the class of indecomposable two-dimensional Landau-Ginzburg theories with (2,2) supersymmetry and central charge c < 6 with the aim of classifying all such theories up to marginal deformations. Our results include cases overlooked in previous classifications. The results are rigorous for three or fewer fields and more generally are rigorous if we assume an extra bound. Numerics suggest that we have the complete set of indecomposable Landau-Ginzburg families with c<6. This set consists of 38 infinite families and a finite list of 418 sporadic cases. The basic tools are classic results of Kreuzer and Skarke on quasi-homogeneous isolated singularities and solutions to certain feasibility integer programming problems.

arXiv comment39 pages and tikz figures, three text files with LG charges included in submission; v2 fixes two sets of charges

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• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Small Landau-Ginzburg theories
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories