Arithmetic and Attractors
| dc.creator | Moore, Gregory | |
| dc.date | 1998-07-13 | |
| dc.date | 2007-02-15 | |
| dc.date.accessioned | 2026-07-07T07:46:48Z | |
| dc.date.available | 2026-07-07T07:46:48Z | |
| dc.description | We study relations between some topics in number theory and supersymmetric black holes. These relations are based on the ``attractor mechanism'' of N=2 supergravity. In IIB string compactification this mechanism singles out certain ``attractor varieties.'' We show that these attractor varieties are constructed from products of elliptic curves with complex multiplication for N=4 and N=8 compactifications. The heterotic dual theories are related to rational conformal field theories. In the case of N=4 theories U-duality inequivalent backgrounds with the same horizon area are counted by the class number of a quadratic imaginary field. The attractor varieties are defined over fields closely related to class fields of the quadratic imaginary field. We discuss some extensions to more general Calabi-Yau compactifications and explore further connections to arithmetic including connections to Kronecker's Jugendtraum and the theory of modular heights. The paper also includes a short review of the attractor mechanism. A much shorter version of the paper summarizing the main points is the companion note entitled ``Attractors and Arithmetic'' (hep-th/9807056). | |
| dc.description | 107pp. harvmac b-mode, 4 figures; minor mistakes, typos corrected. references added;v3: typo fixed, reference added | |
| dc.identifier | https://arxiv.org/abs/hep-th/9807087 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9807087 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123952 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Arithmetic and Attractors | |
| dc.type | text |