Geometric Kac-Moody Modularity

Details Geometric Kac-Moody Modularity Geometric Kac-Moody Modularity

2004-10-18

arxiv.org/abs/hep-th/0410189v1

J.Geom.Phys. 56 (2006) 843-863

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

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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