Supermembranes with Fewer Supersymmetries

The usual supermembrane solution ofD = 11 supergravity interpolates between R11 and AdS4× round S7, has symmetry P3×SO(8) and preserves 1/2 of the spacetime supersymmetries for either orientation of the round S7. Here we show that more general supermembrane solutions may be obtained by replacing the round S7 by any seven-dimensional Einstein space M7. These have symmetry P3 × G, where G is the isometry group of M7. For example, G = SO(5) × SO(3) for the squashed S7. For one orientation of M7, they preserve N/16 spacetime supersymmetries where 1 ≤ N ≤ 8 is the number of Killing spinors on M7; for the opposite orientation they preserve no supersymmetries since then M7 has no Killing spinors. For example N = 1 for the left-squashed S7 owing to its G2 Weyl holonomy, whereas N = 0 for the right-squashed S 7. All these solutions saturate the same Bogomol’nyi bound between the mass and charge. Similar replacements of SD−p−2 by Einstein spacesMD−p−2 yield new super p-brane solutions in other spacetime dimensions D ≤ 11. In particular, simultaneous dimensional reduction of the aboveD = 11 supermembranes on S1 leads to a new class ofD = 10 elementary string solutions which also have fewer supersymmetries. † Research supported in part by NSF Grant PHY-9411543 ‡ Research supported in part by DOE Grant DE-FG05-91-ER40633