Aspects of Collapsing Cycles

TL;DR

This paper explores how cycles in Calabi-Yau backgrounds evolve and degenerate, providing insights into quantum geometry through three specific scenarios involving quantum volume, attractor flows, and topology change.

Contribution

It introduces new perspectives on cycle behavior in Calabi-Yau spaces, linking cycle degeneration to quantum geometric phenomena.

Findings

Cycle degeneration relates to quantum volume changes

Attractor flows influence D-brane stability

Topology change impacts quantum geometric structure

Abstract

Much has been learned about string theory over the last few years by studying properties of cycles and branes in a given background geometry. Here we discuss three situations (quantum volume, attractor flows/D-brane stability, and dynamical topology change) in which cycles in a Calabi-Yau background evolve and/or degenerate in some manner, yielding various insights into aspects of quantum geometry. Based in part on talk given at Strings 2000.