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Albrecht Klemm: Lectures

September 11, 2019
TITLE: CY 3-folds over finite fields, Black hole attractors, and D-brane masses

ABSTRACT: The integer coefficients of the numerator of the Hasse-Weil Zeta function for one parameter Calabi-Yau 3-folds are expected to be Hecke eigenvalues of Siegel modular forms. For rigid CY 3-folds as well as at conifold — and rank two attractor points this numerator contains factors of lower degree, which can be shown to be the Hecke eigenvalues of weight two or four of modular cusp forms of \Gamma_0(N). We show that the Hecke L-function at integer arguments or more generally the periods of these modular forms give the D-brane masses as well as the value and the curvature of the Weil-Peterssen metric at the points. The coefficients of the connection matrix from the integer symplectic basis to a Frobenius basis at the conifold are given by the quasi periods of these modular forms.