Maximal supersymmetry of AdS4 times S7 ($N=4\times 8=32$)

With the membrane Freund-Rubin compactification flux and the required radius ratio, the Killing spinor equation separates into AdS4 and sphere equations with correlated signs. The respective real solution dimensions are four and eight, giving thirty-two. The associated Killing-spinor connections have vanishing curvature for these choices, so arbitrary initial spinor data generate solutions locally; standard global spin structures give the usual maximally supersymmetric background.

// Target: geometry-and-topology.bigb