Geometry of non-supersymmetric three-charge bound states

TL;DR

This paper investigates the geometric structure of non-supersymmetric three-charge microstates, revealing key differences from supersymmetric cases through dimensional reductions and analyzing their singularities and orbifold features.

Contribution

It provides a detailed geometric analysis of non-supersymmetric microstates, highlighting qualitative differences from supersymmetric solutions and examining their singularity structures.

Findings

Five-dimensional solutions have orbifold fixed points breaking supersymmetry.

Four-dimensional solutions feature connected singularities with conical defects.

The geometries cannot be decomposed into separate BPS centers.

Abstract

We study the smooth non-supersymmetric three-charge microstates of Jejjala, Madden, Ross and Titchener [hep-th/0504181] using Kaluza-Klein reductions of the solutions to five and four dimensions. Our aim is to improve our understanding of the relation between these non-supersymmetric solutions and the well-studied supersymmetric cases. We find some surprising qualitative differences. In the five-dimensional description, the solution has orbifold fixed points which break supersymmetry locally, so the geometries cannot be thought of as made up of separate half-BPS centers. In the four-dimensional description, the two singularities in the geometry are connected by a conical singularity, which makes it impossible to treat them independently and assign unambiguous brane charges to these centers.