Department
Physics
Document Type
Article
Publication Date
11-2004
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 conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.
Journal Title
Nuclear Physics B
Journal ISSN
0550-3213
Volume
700
Issue
1
First Page
463
Last Page
489
Digital Object Identifier (DOI)
j.nuclphysb.2004.08.007