八流形上M理论的一个实超势
A real superpotential for M-theory on eight-manifolds
- Skidmore College（斯基德莫尔学院）
- University of Chicago（芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究推导了八流形上M理论的实超势，通过两种方式得到其表达式，证明其临界点方程等价于十一维超对称条件，且在结构增强时可约化为已知结果。
AI中文摘要：
我们研究十一维超引力在八流形上的翘曲紧致化，以得到三维中保持N=1超对称的闵可夫斯基或AdS真空。对于具有局部G₂结构的背景，我们不进行有限卡鲁扎-克莱因截断，而是根据内部几何和通量导出一个离壳实超势泛函。我们通过两种独立方式得到该表达式：从引力微子变分的维数约化，以及从十一维引力微子作用量的约化。我们证明，临界点方程与超势的真空值等价于十一维 Killing 旋量方程所隐含的全部超对称条件。当局部G₂结构增强为全局Spin(7)结构时，我们的结果约化为已知的Spin(7)流形上M理论的超势。
英文摘要：
We study warped compactifications of eleven-dimensional supergravity on eight-manifolds to Minkowski or AdS vacua preserving $N=1$ supersymmetry in three dimensions. For backgrounds characterised by a local G$_2$ structure, we derive an off-shell real superpotential functional in terms of the internal geometry and fluxes without performing a finite Kaluza-Klein truncation. We obtain this expression in two independent ways: from the dimensional reduction of the gravitino variation and from the reduction of the eleven-dimensional gravitino action. We show that the critical-point equations, together with the vacuum value of the superpotential, are equivalent to the full set of supersymmetry conditions implied by the eleven-dimensional Killing spinor equations. When the local G$_2$ structure enhances to a global Spin(7) structure, our result reduces to the known superpotential for M-theory on Spin(7) manifolds.
