 M2-brane supergravity solution

The transverse harmonic function $H$ solves the field equations away from membrane sources. Positive centres contribute $Q_a/|y-y_a{|}^6$ in eight dimensions. Its Killing spinors are $H^{-1/6}{ϵ}_0$ with one oriented membrane projector, giving sixteen supersymmetries. The three-form's sign and membrane orientation must be chosen together.