Accidents in (0,2) Landau-Ginzburg theories

TL;DR

We address the challenge that accidental symmetries in $(0,2)$ LG RG flows can drastically alter IR data and UV/IR mappings. The work develops tools to detect these accidents via the UV F-term couplings modulo field redefinitions, and proposes a toric description of the SCFT deformation space for plain $(0,2)$ LG models, backed by conformal perturbation theory. Through detailed analyses and explicit examples, it demonstrates how accidents affect central charges and operator spectra, and outlines a toric-moduli framework with evidence from plain models and notable limitations in non-plain cases. The results offer a structured approach to classifying $(0,2)$ SCFTs and their heterotic vacua, guiding future explorations of RG flows, marginal deformations, and GLSM realizations.

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.