最小浸没4D超膜
The Minimally Immersed 4D Supermembrane
摘要：
本文总结了文[1]中的一些性质及其与文[2]的关系。我们讨论了具有非平凡中心荷的11维超膜在7维环面流形上的作用量的构造，得到了超膜的作用量（MIM 2），超膜的横坐标是4维Minkowski时空的映射.与11维闵可夫斯基目标空间上的超膜相比，该作用在附加对称下是不变的。LCG中的哈密顿量在黎曼曲面基流形上的共形变换下是不变的。正则化哈密顿量的谱是离散的，具有有限重数。其解决方案是紧凑的。由于拓扑中心荷条件，Susy在四维空间中自发破缺为四个超对称，真空属于N=1的超多重态。当假定目标空间为各向同性7-环面时，势不含任何平坦方向，它在参数的模空间上是稳定的。此外，由于哈密顿量的离散对称性，MIM 2在7-环面上只有7个可能的极小全纯浸入。当这些对称性在目标空间上被识别时，它对应于在具有G2结构的轨道上紧化MIM 2。一旦奇点被解决，它将导致G2流形上的MIM 2的紧化，如[2]所示。
英文摘要：
In this note we summarize some of the properties found in [1], and its relation with [2]. We comment on the construction of the action of the 11D supermembrane with nontrivial central charges minimally immersed on a 7D toroidal manifold is obtained (MIM2).The transverse coordinates to the supermembrane are maps to a 4D Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a 11D Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters. Moreover due to the discrete symmetries of the hamiltonian, there are only 7 possible minimal holomorphic immersions of the MIM2 on the 7-torus. When these symmetries are identified on the target space, it corresponds to compactify the MIM2 on a orbifold with G2 structure. Once the singularities are resolved it leads to the compactification of the MIM2 on a G2 manifold as shown in [2].
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