M2-brane supergravity solution
= M2-brane supergravity solution
{c}
{title2=$ds^2=H^{-2/3}ds^2(\mathbb R^{1,2})+H^{1/3}dy^2$}
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 $H^{-1/6}\epsilon_0$ with one oriented membrane projector, giving sixteen supersymmetries. The three-form's sign and membrane orientation must be chosen together.