Periods for Calabi--Yau and Landau--Ginzburg Vacua

TL;DR

This paper explores the structure of moduli spaces for Calabi-Yau and Landau-Ginzburg models using periods, providing explicit calculations and insights into mirror symmetry in superstring compactifications.

Contribution

It demonstrates how to compute periods explicitly for various Calabi-Yau models and shows how to extract mirror symmetry information from these periods.

Findings

Explicit period calculations for multiple Calabi-Yau classes

Methodology for deriving mirror symmetry data from periods

Enhanced understanding of moduli space structure in superstring theory

Abstract

The complete structure of the moduli space of \cys\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.