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arXiv 2108.02309hep-th
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超引力F理论模型中的电荷完备性和无质量电荷格

Charge completeness and the massless charge lattice in F-theory models of supergravity

David R. Morrison, Washington Taylor

摘要:

我们证明,对于每一个具有F理论描述的6D超引力理论,规范群连通分支的荷完备性(意味着相应电荷晶格中的所有电荷都是由理论中的质量态或无质量态实现的)等价于F理论中关于几何如何通过Mordell编码全局规范理论的标准假设-椭圆纤维化的Weil群。这一结果也适用于4D F-理论结构的规范群的部分,来自截面和7-膜。我们发现,在许多6D F-理论模型的理论的满电荷晶格产生的无质量的带电状态,这发生在每个规范因子的相关异常系数满足一个简单的正性条件。我们描述了许多情况下,这种无质量电荷的充分条件,以及例外的情况下,积极性条件失败,并分析相关的全球结构的规范群和相关的莫德尔-韦尔扭转显式F-理论模型。

英文摘要:

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.

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