Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds

TL;DR

This paper explores the attractor mechanisms in the moduli spaces of Calabi-Yau 3-folds, introducing new classes called attractor varieties and examining their complex and Kähler structures.

Contribution

It introduces the Kähler attractor mechanism and defines Kähler attractor varieties, extending the complex attractor framework within Calabi-Yau moduli spaces.

Findings

Complex attractor varieties are defined via minimizing normalized central charges.

Kähler attractor varieties are introduced through mirror symmetry considerations.

Both types of attractor varieties are expected to have rich geometric structures.

Abstract

We investigate the complex and K\"ahler attractor mechanisms of moduli spaces of Calabi-Yau 3-folds. The complex attractor mechanism was previously studied by Ferrara-Kallosh-Strominger, Moore and others in string theory. It is concerned with the minimizing problems of the normalized central charges of 3-cycles and defines a new interesting class of Calabi-Yau 3-folds called, the complex attractor varieties. In light of mirror symmetry, we introduce the K\"ahler attractor mechanism and define the K\"ahler attractor varieties. The complex and K\"ahler attractor varieties are expected to possess very rich structures, in particular certain complex and K\"ahler rigidities.