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arXiv 0810.2685hep-th
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关于Calabi-Yau五折的M-理论

M-theory on Calabi-Yau Five-Folds

Alexander S. Haupt, Andre Lukas, K. S. Stelle

备注：
82 pages, JHEP3 style. v2: acknowledgements and references added, signs and typos corrected, revised sections 4-6 and B.4. Final version accepted for publication
发表信息：
JHEP 0905:069,2009
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摘要：

本文研究了Calabi-Yau五重上M-理论的紧化以及由此得到的N=2超力学理论。通过从11维显式约化，包括玻色子和费米子项，我们计算了一维有效作用量，并表明它可以从N=2的超空间作用量导出。我们发现，Kahler和复杂的结构模的五倍驻留在2a和2b超多重态，分别。受约束的2a超多重态产生于M理论三重态的零模，并导致2a和2b多重态之间的交叉耦合。从11维引力子的（1，3）扇区产生的费米零模没有玻色子超伴子，只能用一维的纯费米超多重态来描述。我们还研究了通量的包含，并讨论了一维N=2超对称的标量势的一致性，以及如何用超势来描述它。这个超势也可以从我们提出的Gukov型公式中得到。通过解F项方程得到的超对称真空，由于这个标量势的形式，总是具有消失的真空能量。我们表明，这种超对称的解决方案存在特定的例子。两个重要的附录发展了卡-丘五重的拓扑和几何，以及一维N=2超对称和超引力的结构，达到了我们的目的所需的一般性水平。

英文摘要：

We study the compactification of M-theory on Calabi-Yau five-folds and the resulting N=2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an N=2 super-space action. We find that the Kahler and complex structure moduli of the five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1,3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional N=2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukov-type formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional N=2 supersymmetry and supergravity to the level of generality required for our purposes.

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