A detailed case study of the rigid limit in Special K\"ahler geometry using K3

TL;DR

This paper investigates the rigid limit of N=2 supergravity through detailed analysis of Calabi-Yau threefolds with K3 fibrations, focusing on singular points in moduli space and their relation to special K"ahler geometry.

Contribution

It provides a comprehensive case study of the rigid limit in special K"ahler geometry using K3 fibrations in Calabi-Yau manifolds, highlighting the geometric transition to rigid supersymmetry.

Findings

Identification of the fibration parameter with the Riemann surface coordinate

Explicit analysis of singular points in moduli space

Connection between Calabi-Yau geometry and rigid N=2 supersymmetry

Abstract

This is a r\'esum\'e of an extensive investigation of some examples in which one obtains the rigid limit of N=2 supergravity by means of an expansion around singular points in the moduli space of a Calabi-Yau 3-fold. We make extensive use of the K3 fibration of the Calabi-Yau manifolds which are considered. At the end the fibration parameter becomes the coordinate of the Riemann surface whose moduli space realises rigid N=2 supersymmetry.