Complex Multiplication of Exactly Solvable Calabi-Yau Varieties
arXiv:hep-th/0312319 · doi:10.1016/j.nuclphysb.2004.08.007
Abstract
We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi-Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and the conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.
arXiv comment44 pages
References in corpus (7)
- Dilogarithm identities
- Arithmetic and Attractors
- Dilogarithm Identities in Conformal Field Theory
- Rational Conformal Field Theories and Complex Multiplication
- The Shimura-Taniyama Conjecture and Conformal Field Theory
- Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory
- Complex Multiplication Symmetry of Black Hole Attractors
Cited by in corpus (6)
- Les Houches Lectures on Strings and Arithmetic
- The Langlands Program and String Modular K3 Surfaces
- Emergent spacetime from modular motives
- Arithmetic Spacetime Geometry from String Theory
- Geometric Kac-Moody Modularity
- String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication