Title

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

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