Complex Multiplication Symmetry of Black Hole Attractors

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.

28 pages

References in corpus (1)

• Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory

Cited by in corpus (7)

• Les Houches Lectures on Strings and Arithmetic
• The Langlands Program and String Modular K3 Surfaces
• Two-Center Black Holes, Qubits and Elliptic Curves
• Arithmetic Spacetime Geometry from String Theory
• Geometric Kac-Moody Modularity
• Complex Multiplication of Exactly Solvable Calabi-Yau Varieties
• String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication