Accidents in (0,2) Landau-Ginzburg theories

Abstract

We study the role of accidental symmetries in two-dimensional (0,2) superconformal field theories obtained by RG flow from (0,2) Landau-Ginzburg theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) Landau-Ginzburg models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. We also give a self-contained discussion of aspects of (0,2) conformal perturbation theory.

arXiv comment37 pages; expanded conformal perturbation theory discussion in v2; fixed an accident in section 3.5 in v3

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• A 2d (0,2) appetizer
• Wilson surfaces in M5-branes
• Worldsheet instantons and (0,2) linear models
• K stability and stability of chiral ring
• Landau-Ginzburg skeletons
• (0,2) hybrid models
• Relevant deformations and c-extremization
• Small Landau-Ginzburg theories
• Fixed points of (0,2) Landau-Ginzburg renormalization group flows and the chiral algebra
• Making supersymmetric connected N =(0,2) Sigma Models
• A (0,2) mirror duality
• Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications