Freund–Rubin compactification

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11D supergravity contains a 3-form field C. It also contains an electric 2-brane (M2) and a magnetic 5-brane (M5) under C. These branes are BPS states and they are also black branes. Their near horizon metrics are given by AdS4×S7 and AdS7× S4 respectively. These geometries contain a nonzero four-flux which gives rise to a nonzero Ricci curvature. They are called Freund–Rubin compactifications.