Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-11-22
Phys.Lett.B371:206-214,1996
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, Latex, no figures
Scientific paper
10.1016/0370-2693(95)01606-6
The usual supermembrane solution of $D=11$ supergravity interpolates between $R^{11}$ and $AdS_4 \times round~S^7$, has symmetry $P_3 \times SO(8)$ 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 $P_3 \times G$, where $G$ is the isometry group of $M^7$. For example, $G=SO(5) \times SO(3)$ 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.
Duff M. J.
Lu Hai
Pope Christopher N.
Sezgin Ergin
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