Supermembranes with fewer supersymmetries

M. J. Duff; H. Lu; C. N. Pope; E. Sezgin

doi:10.1016/0370-2693(95)01606-6

paper

Supermembranes with fewer supersymmetries

arXiv:hep-th/9511162 · doi:10.1016/0370-2693(95)01606-6

Abstract

The usual supermembrane solution of $D = 11$ supergravity interpolates between $R^{11}$ and $A d S_{4} \times r o u n d S^{7}$ , has symmetry $P_{3} \times S O (8)$ 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 $P_{3} \times G$ , where $G$ is the isometry group of $M^{7}$ . For example, $G = S O (5) \times S O (3)$ for the squashed $S^{7}$ . For one orientation of $M^{7}$ , they preserve $N /16$ spacetime supersymmetries where $1 \leq N \leq 8$ 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 $D \leq 11$ . 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.

14 pages, Latex, no figures

Supermembranes with fewer supersymmetries

Abstract

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