The Spin of the M2-Brane and Spin-Spin Interactions via Probe Techniques

TL;DR

This paper constructs supergravity solutions for spinning M2-branes, analyzes their spin properties, and investigates spin-spin interactions using probe techniques, revealing novel forces and fermionic effects in M-theory.

Contribution

It introduces explicit spinning M2-brane solutions with non-standard features and studies their interactions, including spin-spin forces, via probe methods.

Findings

Spinning M2-branes have non-Kerr type metrics with gravitino presence.

Static spin-spin forces exist between branes and anti-branes.

Probe analysis uncovers gravitational and fermionic spin interactions.

Abstract

The 256 dimensional M2-brane multiplet contains solitons of many different intrinsic spins. Using the broken supersymmetry transformations of the M2-brane, we find supergravity solutions which explicitly display these spins. This amounts to quantizing the fermionic zero modes and computing the back reaction on the metric and gauge potential. These spacetime fields are therefore operator valued and acquire a conventional classical meaning only after taking expectations in given BPS states. Our spinning spacetimes are not of the standard Kerr form -- there is a non-vanishing gravitino. Nevertheless, the solutions have angular momentum and magnetic dipole moments with a g-factor of 2. We use probe techniques to study scattering of spinning BPS M2-branes. The static interactions cancel between like-sign branes at leading order, but there are static spin-spin forces between branes and anti-branes. The general probe-background Lagrangian contains gravitational spin-spin and magnetic dipole-dipole forces, as well as gravitino exchanges which allow branes to change fermion number.