Periods and Duality Symmetries in Calabi-Yau Compactifications

TL;DR

This paper analyzes the period structure of Calabi-Yau manifolds to identify duality symmetries, mirror maps, and non-perturbative corrections, enhancing understanding of string compactifications and automorphic functions.

Contribution

It provides explicit derivations of period structures, duality group generators, and mirror maps for one-modulus Calabi-Yau manifolds, including non-perturbative Yukawa corrections.

Findings

Derived period structures for specific Calabi-Yau manifolds

Identified generators of duality groups and mirror maps

Computed non-perturbative Yukawa coupling corrections

Abstract

We derive the period structure of several one-modulus Calabi-Yau manifolds. With this knowledge we then obtain the generators of the duality group and the mirror map that defines the physical variable $t$ representing the radius of compactification. We also describe the fundamental region of $t$ and discuss its relation with automorphic functions. As a byproduct of our analysis we compute the non-perturbative corrections of Yukawa couplings.