Geometric Kac–Moody Modularity
Department
Physics
Document Type
Article
Publication Date
5-2006
Abstract
It is shown how the arithmetic structure of algebraic curves encoded in the Hasse–Weil L-function can be related to affine Kac–Moody algebras. This result is useful in relating the arithmetic geometry of Calabi–Yau varieties to the underlying exactly solvable theory. In the case of the genus three Fermat curve we identify the Hasse–Weil L-function with the Mellin transform of the twist of a number theoretic modular form derived from the string function of a non-twisted affine Lie algebra. The twist character is associated to the number field of quantum dimensions of the conformal field theory.
Journal Title
Journal of Geometry and Physics
Journal ISSN
0393-0440
Volume
56
Issue
5
First Page
843
Last Page
863
Digital Object Identifier (DOI)
10.1016/j.geomphys.2005.05.003
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