The Ooguri-Vafa metric, holomorphic discs and wall-crossing

Determinants of the Calabi-Yau Metrics on K3 Surfaces, Discriminants, Theta Lifts and Counting Problems in the A and B Models

The Dedekind eta functions plays important role in different branches of Mathematics and Theoretical Physics. One way to construct Dedekind Eta function to use the explicit formula (Kroncker limit formula) for the regularized determinants of the Laplacian of the flat metric acting of (0,1) forms on elliptic curves. The holomorphic part of the regularized determinant is the Dedekind eta functions. In this paper we generalized the above approach to the case of K3 surfaces. We give an explicit formula of the regularized determinants of the Laplacians of Calabi Yau metrics on K3 Surfaces, followin…