= Maximal supersymmetry of AdS4 times S7
{title2=$N=4\times8=32$}
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
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