World-sheet Stability of (0,2) Linear Sigma Models

TL;DR

This work addresses whether world-sheet instantons destabilize $(0,2)$ theories by generating a non-perturbative superpotential. It combines explicit GLSM constructions without tree-level superpotentials with a general Konishi anomaly analysis to show that no non-perturbative worldsheet superpotential $S_J$ can arise, and extends the result to cases with tree-level superpotentials. Consequently, there is no corresponding space-time instability in perturbatively conformal theories, reinforcing a robust non-renormalization structure for $(0,2)$ models. The results integrate instanton zero-mode counting, anomaly considerations, and Bogomolnyi arguments to establish broad world-sheet stability in these theories.

Abstract

We argue that two-dimensional (0,2) gauged linear sigma models are not destabilized by instanton generated world-sheet superpotentials. We construct several examples where we show this to be true. The general proof is based on the Konishi anomaly for (0,2) theories.