Geometry of (0,2) Landau-Ginzburg Orbifolds

TL;DR

The paper develops a comprehensive framework for (0,2) Landau-Ginzburg orbifolds, centered on the elliptic genus as a topological probe that connects LG orbifolds to (0,2) sigma models. It constructs the LG elliptic genus from left-right $U(1)$ charges, BRST cohomology, and Koszul homology, and establishes modular properties and residue-type expressions. Applying this to Distler-Kachru models, the authors show that LG calculations reproduce sigma-model predictions even for singular Calabi–Yau spaces, enabling generation-number computations and a detailed ground-state analysis via Born-Oppenheimer methods. The results reinforce the LG-sigma-model correspondence in the (0,2) setting and highlight algebraic-geometric structures underpinning untwisted sectors, with potential extensions to resolved geometries and (0,2) dualities.

Abstract

Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma models. Our formalism gives an easy way to calculate the generation numbers for lots of Distler-Kachru models even if they are based on singular Calabi-Yau spaces. We also make some general remarks on the Born-Oppenheimer calculation of the ground states elucidating its mathematical meaning in the untwisted sector. For Distler-Kachru models based on non-singular Calabi-Yau spaces we show that there exist `residue' type formulas of the elliptic genera as well.