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arXiv · hep-th/0410189

Geometric Kac-Moody Modularity

Monika Lynker·Rolf Schimmrigk
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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.

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Monika Lynker, Rolf Schimmrigk. 2004-10-18. Geometric Kac-Moody Modularity. https://doi.org/10.1016/j.geomphys.2005.05.003

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