Some Features of (0,2) Moduli Space

TL;DR

This paper explores the structure of the (0,2) Calabi-Yau moduli space, revealing how different models can intersect along sub-loci, indicating a complex, multicritical structure with potential implications for F-theory.

Contribution

It demonstrates how (0,2) models with different data can meet in moduli space, including cases with topologically distinct Calabi-Yau bases, extending previous singular space analyses.

Findings

Models with different (0,2) data can meet along sub-loci.

Smooth Calabi-Yau bases can be topologically distinct.

Indicates a multicritical structure in moduli space.

Abstract

We discuss some aspects of perturbative $(0,2)$ Calabi-Yau moduli space. In particular, we show how models with different $(0,2)$ data can meet along various sub-loci in their moduli space. In the simplest examples, the models differ by the choice of desingularization of a holomorphic V-bundle over the same resolved Calabi-Yau base while in more complicated examples, even the smooth Calabi-Yau base manifolds can be topologically distinct. These latter examples extend and clarify a previous observation which was limited to singular Calabi-Yau spaces and seem to indicate a multicritical structure in moduli space. This should have a natural F-theory counterpart in terms of the moduli space of Calabi-Yau four-folds.