# Topological Sources of Soliton Mass and Supersymmetry Breaking

## TL;DR

This paper explores how topological features in five-dimensional supergravity solutions lead to supersymmetry breaking and BPS-bound violations, analyzing specific geometries and their mass formulas.

## Contribution

It derives Smarr formulas for complex supergravity solutions and links topological structures to supersymmetry breaking and BPS-bound violations.

## Key findings

- Topological features influence supersymmetry breaking.
- Holonomy affects the BPS-bound in these solutions.
- Bulk terms contribute to mass and supersymmetry violation.

## Abstract

We derive the Smarr formulae for two five-dimensional solutions of supergravity, which are asymptotically R^(1,3)xS^1; in particular, one has a magnetic bolt in its center, and one is a two-center solution. We show for both spacetimes that supersymmetry - and so the BPS-bound - is broken by the holonomy and how each topological feature of a space-like hypersurface enters Smarr's mass formula, with emphasis on the ones that give rise to the stated violation of the BPS-bound. In this light, we question if any violating extra-mass term in a spacetime with such asymptotics is only evident in the ADM mass while the Komar mass per se tries to preserve BPS. Finally, we derive the cohomological fluxes for each situation and examine in a more general fashion how the breaking of supersymmetry - and so the BPS-bound violation - is associated with their topologies. In the second (and more complicated) scenario, we especially focus on the compact cycle linking the centers, and the contribution of non-vanishing bulk terms in the mass formula to the breaking of supersymmetry.