The Breakdown of Topology at Small Scales

TL;DR

This paper explores how the Zariski topology on a space can effectively break down at small scales due to D-brane decay, aligning with phase transitions in Calabi-Yau moduli spaces and approaching non-geometric phases.

Contribution

It proposes a mechanism linking D-brane decay to the breakdown of topology at small scales, connecting physical decay processes with geometric phase transitions.

Findings

Topology appears to break down near non-geometric phases.

The proposed mechanism aligns with Calabi-Yau moduli space phase picture.

Limitations of the model are discussed.

Abstract

We discuss how a topology (the Zariski topology) on a space can appear to break down at small distances due to D-brane decay. The mechanism proposed coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The topology breaks down as one approaches non-geometric phases. This picture is not without its limitations, which are also discussed.