Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces

TL;DR

This paper advances the understanding of mirror symmetry for complete intersection Calabi-Yau spaces by developing new methods to compute Yukawa couplings and prepotentials, including cases with higher-dimensional moduli spaces and topology changes.

Contribution

It introduces a novel approach to derive instanton-corrected Yukawa couplings from Picard-Fuchs solutions for complete intersections, providing explicit formulas for the prepotential in various models.

Findings

Closed formulas for prepotentials in complete intersections.

Application to three-generation models relevant for phenomenology.

Analysis of topology change in Calabi-Yau moduli spaces.

Abstract

We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton-corrected Yukawa couplings, and the topological one-loop partition function to the case of complete intersections with higher-dimensional moduli spaces. We will develop a new method of obtaining the instanton-corrected Yukawa couplings through a close study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the K\"ahler moduli fields induced from the ambient space for all complete intersections in non singular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models that are found in this class. We also apply our method to solve the simplest model in which a topology change was observed and discuss examples of complete intersections in singular ambient spaces.