Arithmetic of Calabi–Yau varieties and rational conformal field theory
✍ Scribed by Rolf Schimmrigk
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 122 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0393-0440
No coin nor oath required. For personal study only.
✦ Synopsis
It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and the underlying conformal field theory. Specifically, it is pointed out how the algebraic number field determined by the fusion rules of the conformal field theory can be derived from the number theoretic structure of the cohomological Hasse-Weil L-function determined by Artin's congruent zeta function of the algebraic variety. In this context, a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.