Non-compact Gepner Models, Landau-Ginzburg Orbifolds and Mirror Symmetry

TL;DR

This paper develops an orbifolded Landau-Ginzburg framework for non-compact Gepner models, enabling geometric and mirror symmetry analysis, and investigates moduli counting in large level limits.

Contribution

It introduces a Landau-Ginzburg description for non-compact Gepner models and extends mirror symmetry constructions to these models.

Findings

Landau-Ginzburg description clarifies singularity geometry

Mirror pairs are constructed via adapted Greene-Plesser method

Moduli counting differs from toric predictions in large level limit

Abstract

We study non-compact Gepner models that preserve sixteen or eight supercharges in type II string theories. In particular, we develop an orbifolded Landau-Ginzburg description of these models analogous to the Landau-Ginzburg formulation of compact Gepner models. The Landau-Ginzburg description provides an easy and direct access to the geometry of the singularity associated to the non-compact Gepner models. Using these tools, we are able to give an intuitive account of the chiral rings of the models, and of the massless moduli in particular. By studying orbifolds of the singular linear dilaton models, we describe mirror pairs of non-compact Gepner models by suitably adapting the Greene-Plesser construction of mirror pairs for the compact case. For particular models, we take a large level, low curvature limit in which we can analyze corrections to a flat space orbifold approximation of the non-compact Gepner models. This gives rise to a counting of moduli which differs from the toric counting in a subtle way.