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Geometric Kac-Moody Modularity

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arxiv hep-th/0410189 v1 pith:B3THARAV submitted 2004-10-18 hep-th

Monika Lynker , Rolf Schimmrigk This is my paper
classification hep-th
keywords affinearithmeticfieldhasse-weilkac-moodyl-functionnumbertheory
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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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    Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.

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