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.Comment: 28 page

Andrianopoli

Behrndt

Billo

Blasius

Candelas

Ceresole

Deligne

Faddeev

Ferrara

Gross

Gukov

Jannsen

Larsen

Miller

Monika Lynker

Moore

Neukirch

Ramakrishnan

Rohrlich

Rolf Schimmrigk

Sabra

Saito

Schimmrigk

Shimura

Shioda

Silverman

Strominger

Vipul Periwal

Weil

Nuclear Physics B

English

arXiv

Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold. This would be inconsistent with known properties of black holes. Supersymmetric black holes appear to evade this inconsistency by having moduli fields that flow to fixed points in the moduli space that depend only on the charges of the black hole. Moore observed in the case of compactifications with elliptic curve factors that these fixed points are arithmetic, corresponding to curves with complex multiplication. The main goal of this talk is to explore the possibility of generalizing such a characterization to Calabi-Yau varieties with finite fundamental groups

Lynker, Monika

Periwal, Vipul

Schimmrigk, Rolf

DigitalCommons@Kennesaw State University

Black Hole Attractor Varieties and Complex Multiplication

Crossref

Black hole attractor varieties and complex multiplication

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

IUScholarWorks (Indiana University)