A product compactification supported by a four-form proportional to one factor's volume form. For the maximally supersymmetric membrane throat, the other factor is a round and the radii obey . The flux links the curvature scales through the supergravity field equations.
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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Freund–Rubin compactification is a method used in the context of string theory and higher-dimensional theories of gravity, particularly in relation to the compactification of extra dimensions. The concept was introduced by Justin Freund and Marvin Rubin in the early 1980s. In string theory and related theories, we often encounter scenarios where the observable universe is modeled as a four-dimensional spacetime (3 spatial dimensions plus time) embedded within a higher-dimensional space.