Small Volumes in Compactified String Theory

TL;DR

This paper explores the quantum geometry of Calabi-Yau compactifications, focusing on quantum volume and its role in understanding nonperturbative effects in string theory.

Contribution

It introduces the concept of quantum volume in the context of Calabi-Yau degenerations and analyzes its unique features compared to classical volume.

Findings

Quantum volume exhibits unusual properties compared to classical volume.

Quantum volume helps identify loci in moduli space with nonperturbative effects.

The paper clarifies the relationship between geometry and physics in string compactifications.

Abstract

We discuss some of the classical and quantum geometry associated to the degeneration of cycles within a Calabi-Yau compactification. In particular, we focus on the definition and properties of quantum volume, especially as it applies to identifying the physics associated to loci in moduli space where nonperturbative effects become manifest. We discuss some unusual features of quantum volume relative to its classical counterpart.