Complex Multiplication Symmetry of Black Hole Attractors

TL;DR

This paper generalizes Moore's complex multiplication symmetry of black hole attractors from toroidal to Calabi-Yau compactifications, proposing a universal framework using motives and Deligne's period conjecture to study their arithmetic properties.

Contribution

It extends the complex multiplication symmetry concept to Calabi-Yau compactifications with finite fundamental groups, introducing a motive-based approach for their arithmetic analysis.

Findings

Generalization of Moore's observation to Calabi-Yau cases

Introduction of a motive-based framework for attractor varieties

Potential link to Deligne's period conjecture for arithmetic properties

Abstract

We show how Moore's observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite fundamental groups. This generalization leads to an alternative general framework in terms of motives associated to a Calabi-Yau variety in which it is possible to address the arithmetic nature of the attractor varieties in a universal way via Deligne's period conjecture.