Collapsing D-Branes in Calabi-Yau Moduli Space: I

TL;DR

This paper investigates how D-branes in Calabi-Yau manifolds behave near phase transitions, revealing new features in quantum volumes and implications for arithmetic geometry, extending beyond previous specific case studies.

Contribution

It provides a general analysis of D-brane quantum volumes near phase transitions, uncovering new phenomena beyond prior focused studies on specific examples.

Findings

Identification of new qualitative features in D-brane quantum volumes near phase transitions

Extension of analysis beyond two-cycles and specific Calabi-Yau examples

Implications for arithmetic geometry related to Calabi-Yau moduli

Abstract

We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low energy physical descriptions of the resulting string theory. Whereas previous studies have solely considered quantum volumes in the context of two-cycles in perturbative string theory or D-branes in the specific example of the quintic hypersurface, we work more generally and find qualitatively new features. On the mathematical side, as we briefly note, our work has some interesting implications for certain issues in arithmetics.