Geometry of non-supersymmetric three-charge bound states

TL;DR

The paper analyzes non-supersymmetric three-charge microstate geometries by performing Kaluza-Klein reductions to five and four dimensions and embedding the solutions in M-theory, to compare with supersymmetric constructions. It reveals two key surprises: in five dimensions the two centers are described by non-supersymmetric orbifold fixed points, and upon reduction to four dimensions a conical line connects the centers with fractional gauge holonomies, blocking unambiguous brane charge attribution. These findings show the familiar 'half-BPS atom' picture from SUSY microstate geometries does not generalize to the non-supersymmetric case, highlighting fundamental structural differences and signaling substantial challenges for constructing general non-SUSY multi-center solutions. The work also clarifies the role of holonomies and orbifold singularities in shaping the local and global structure of the solutions, with implications for interpreting non-BPS microstates in terms of brane configurations.

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.