7d spherical space forms -- table

$N$ Killing spinors on spherical space form $S^7/\widehat{G}$ | $\phantom{AA}\widehat{G} =$ | spin-lift of subgroup of isometry group of 7-sphere | 3d superconformal gauge field theory on back M2-branes with near horizon geometry $AdS_4 \times S^7/\widehat{G}$ |
---|---|---|---|

$\phantom{AA}N = 8\phantom{AA}$ | $\phantom{AA}\mathbb{Z}_2$ | cyclic group of order 2 | BLG model |

$\phantom{AA}N = 7\phantom{AA}$ | — | — | — |

$\phantom{AA}N = 6\phantom{AA}$ | $\phantom{AA}\mathbb{Z}_{k\gt 2}$ | cyclic group | ABJM model |

$\phantom{AA}N = 5\phantom{AA}$ | $\phantom{AA}2 D_{k+2}$ $2 T$, $2 O$, $2 I$ | binary dihedral group, binary tetrahedral group, binary octahedral group, binary icosahedral group | (HLLLP 08a, BHRSS 08) |

$\phantom{AA}N = 4\phantom{AA}$ | $\phantom{A}2 D_{k+2}$ $2 O$, $2 I$ | binary dihedral group, binary octahedral group, binary icosahedral group | (HLLLP 08b, Chen-Wu 10) |

- José Figueroa-O'Farrill et al. 2009 (arXiv:0909.0163, pdf slides)