The Attractor Conjecture for Calabi-Yau variations of Hodge structures

TL;DR

This paper proves Moore's Attractor Conjecture for certain Calabi-Yau moduli spaces, showing attractor points are CM points, and explores non-BPS attractors and their geometric descriptions.

Contribution

It establishes the attractor points as CM points in Shimura varieties and analyzes non-BPS attractors in various symmetric spaces, providing new geometric insights.

Findings

Attractor points are CM points in specific moduli spaces.

Identification of non-BPS attractors in non-hermitian symmetric spaces.

Explicit geometric description of non-BPS attractors in simple cases.

Abstract

We study attractor points for Calabi-Yau variations of Hodge structures. In particular, for certain moduli spaces which are Shimura varieties, we prove that the attractor points are CM points, thus proving Moore's Attractor Conjecture in these cases. We also study non-BPS examples of attractors, obtaining special points on locally symmetric spaces without hermitian structures, as well as locally symmetric spaces inside Shimura varieties; for the latter we point out a possible analogy with subspaces studied by Goresky-Tai. Finally we give an explicit geometric description of non-BPS attractors in the simplest case.