BPS Force Balances via Spin-Spin Interactions

TL;DR

This paper investigates how spin-spin interactions influence force balances in BPS soliton systems, revealing cancellations between gravitational and magnetic forces that enable static multi-soliton configurations.

Contribution

It introduces a detailed analysis of spin-spin force cancellations in BPS solitons within IWP and superpartner spacetimes, highlighting new force balance mechanisms.

Findings

Spin-spin and magnetic dipole-dipole force cancellations enable static solutions.

Analysis of force interactions using probe particle methods.

Identification of coupling between curvature and spin in soliton dynamics.

Abstract

We study two systems of BPS solitons in which spin-spin interactions are important in establishing the force balances which allow static, multi-soliton solutions to exist. Solitons in the Israel-Wilson-Perjes (IWP) spacetimes each carry arbitrary, classical angular momenta. Solitons in the Aichelburg-Embacher "superpartner" spacetimes carry quantum mechanical spin, which originates in the zero-modes of the gravitino field of N=2 supergravity in an extreme Reissner-Nordstrom background. In each case we find a cancellation between gravitational spin-spin and magnetic dipole-dipole forces, in addition to the usual one between Newtonian gravitational attraction and Coulombic electrostatic repulsion. In both cases, we analyze the forces between two solitons by treating one of the solitons as a probe or test particle, with the appropriate properties, moving in the background of the other. In the IWP case, the equation of motion for a spinning test particle, originally due to Papapetrou, includes a coupling between the background curvature and the spin of the test particle. In the superpartner case, the relevant equation of motion follows from a kappa-symmetric superparticle action.