Domain Walls on Singularities

TL;DR

This paper studies domain walls on specific singularities, showing their BPS or non-BPS nature depending on the resolution, and their ability to connect vacua with monopoles and vortices.

Contribution

It introduces a detailed analysis of domain walls on $A_2$ and $A_3$ singularities, highlighting their BPS properties and interpolating capabilities.

Findings

BPS domain walls exist on resolved singularities.

Non-BPS walls occur on deformed, fibered singularities.

Domain walls can connect vacua supporting monopoles and vortices.

Abstract

We describe domain walls that live on $A_2$ and $A_3$ singularities. The walls are BPS if the singularity is resolved and non--BPS if it is deformed and fibered. We show that these domain walls may interpolate between vacua that support monopoles and/or vortices.