The Revival of (0,2) Linear Sigma Models

TL;DR

The Revival of (0,2) Linear Sigma Models surveys how gauged linear sigma models illuminate the worldsheet description of heterotic compactifications beyond the supergravity regime. It develops (0,2) GLSMs, including V- and M-models, and their A/2 and B/2 twists, to compute protected quantities such as Yukawas and quantum cohomology; it also introduces the Coulomb-branch and quantum-restriction formalisms that relate M- and V-model correlators. A key emphasis is the construction of mirror maps for reflexively plain (0,2) models and the analysis of singular loci signaling bundle or geometry degenerations. The work highlights how Landau-Ginzburg phases and topology-change phenomena fit into the (0,2) landscape, and outlines remaining challenges in extending mirror symmetry beyond restricted classes and in determining the full Kähler potential. Overall, the paper argues that (0,2) GLSMs provide a robust, computable framework to explore α′-corrected heterotic vacua and their phenomenology, connecting worldsheet dynamics to spacetime physics through exact, topologically protected data.

Abstract

Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet description remains largely unexplored. We review recent work in developing linear sigma model techniques aimed at elucidating the underlying worldsheet description.