Supermembranes with fewer supersymmetries

Abstract

The usual supermembrane solution of D = 11 supergravity interpolates between R 11 and AdS 4 × round R 7, has symmetry P 3 × SO(8) and preserves 1 2 of the spacetime supersymmetries for either orientation of the round S 7. Here we show that more general supermembrane solutions may be obtained by replacing the round S 7 by any seven-dimensional Einstein space M 7. These have symmetry P 3 × G, where G is the isometry group of M 7. For example, G = SO(5) × SO(3) for the squashed S 7. For one orientation of M 7, they preserve N 16 spacetime supersymmetries where 1 ≤ N ≤ 8 is the number of Killing spinors on M 7; for the opposite orientation they preserve no supersymmetries since then M 7 has no Killing spinors. For example N = 1 for the left-squashed S 7 owing to its G 2 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 S D- p-2 by Einstein spaces M D- p-2 yield new super p-brane solutions in other spacetime dimensions D ≤ 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S 1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.