Spin of the M2-brane and spin-spin interactions via probe techniques - art. no. 084007.

The 256-dimensional M2-brane multiplet contains solitons of many different intrinsic spins. Using the broken supersymmetry transformations of the M2-b rane, 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 an there fore operator valued and acquire a conventional classical meaning only afte r taking expectations in given BPS states. Our spinning spacetimes are not of the standard Kerr form-there is a nonvanishing gravitino. Nevertheless, the solutions have angular momentum and magnetic dipole moments with a g fa ctor of 2. We use probe techniques to study scattering of spinning BPS M2-b ranes. The static interactions cancel between like-sign branes at leading o rder, but there are static spin-spin forces between branes and antibranes. The general probe-background Lagrangian contains gravitational spin-spin an d magnetic dipole-dipole forces, as well as gravitino exchanges which allow branes to change fermion number. [S0556-2821(99)04606-8].