String Quantum Symmetries From Picard-Fuchs Equations And Their Monodromy

TL;DR

This paper explores how the geometry of Calabi-Yau moduli spaces, crucial for string theory compactifications, can be fully described by Picard-Fuchs equations governing period integrals.

Contribution

It demonstrates that the entire moduli space geometry of Calabi-Yau compactifications is encoded in Picard-Fuchs equations for their periods.

Findings

Moduli space geometry is determined by Picard-Fuchs equations.

The approach links local and global properties of the moduli space.

Provides a framework for analyzing string compactifications.

Abstract

Local and global properties of the moduli space of Calabi--Yau type compactifications determine the low energy parameters of the string effective action. We show that the moduli space geometry is entirely encoded in the Picard--Fuchs equations for the periods of the Calabi--Yau $H^{(3)}$--cohomology.