Geometry of (0,2) Landau-Ginzburg Orbifolds

TL;DR

This paper explores the mathematical structure of (0,2) Landau-Ginzburg orbifolds, providing methods to compute elliptic genera and generation numbers, and compares these with sigma model results, especially for models related to Calabi-Yau spaces.

Contribution

It introduces a formalism for calculating elliptic genera and generation numbers in (0,2) Landau-Ginzburg orbifolds, including models based on singular and non-singular Calabi-Yau spaces.

Findings

Elliptic genera are computed for general (0,2) models.

Comparison with (0,2) sigma models confirms consistency.

Residue formulas for elliptic genera are established for non-singular Calabi-Yau cases.

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.