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arXiv 2311.03337hep-th
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六维中新的无反常超引力

New anomaly free supergravities in six dimensions

Katrin Becker, Alex Kehagias, Ergin Sezgin, David Tennyson, Avraam Violaris

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42 pp + 33 pp apendix, 3 figures, 2 tables
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AI总结：

本研究采用图形法和秩法拓展搜索六维无反常$N=(1,0)$超引力，得到大量非规范无反常理论，在$n_T=1$的$R$对称规范模型中发现6个新模型，并证明特定非规范模型类的完备性。

摘要：

我们通过两种不同的方法——我们称之为图形法和秩法——对六维中与物质耦合的无反常$N=(1,0)$超引力开展了拓展搜索。在图形法中，无反常模型由被称为节点的单规范群模型构建而成，这类模型仅可能存在引力反常。我们搜索了规范群为$G_1\times...\times G_n$（其中$n=1,2,...$，即因子数量任意）以及规范群为$G_1\times...\times G_n \times U(1)_R$（其中$n=1,2,3$，且$U(1)_R$为$R$对称群）的无反常理论。虽然我们主要考虑张量多重态数$n_T=1$的模型，但也给出了$n_T\ne 1$且带电超多重态数量不受约束情况下的部分结果。我们发现了大量非规范的无反常理论。然而，在$n_T=1$的$R$对称规范模型中，除了三个已知的具有$G_1\times G_2 \times U(1)_R$型对称性的无反常理论外，我们仅发现了六个新的、具有$G_1\times G_2\times G_3 \times U(1)_R$形式对称群的显著无反常模型。在$n_T=1$的非规范模型情形中，排除低秩群因子且仅考虑低阶表示的情况下，我们找到了所有的无反常理论。值得注意的是，这类理论中的群因子数量不超过四个。该情形下的完备性证明依赖于我们建立的一个参数界，该参数用于表征非单态超多重态数量与规范群维度之间的差值。

英文摘要：

An extended search for anomaly free matter coupled $N=(1,0)$ supergravity in six dimension is carried out by two different methods which we refer to as the graphical and rank methods. In the graphical method the anomaly free models are built from single gauge group models, called nodes, which can only have gravitational anomalies. We search for anomaly free theories with gauge groups $G_1\times...\times G_n$ with $n=1,2,...$ (any number of factors) and $G_1\times...\times G_n \times U(1)_R$ where $n=1,2,3$ and $U(1)_R$ is the $R$-symmetry group. While we primarily consider models with the tensor multiplet number $n_T=1$, we also provide some results for $n_T\ne 1$ with an unconstrained number of charged hypermultiplets. We find a large number of ungauged anomaly free theories. However, in the case of $R$-symmetry gauged models with $n_T=1$, in addition to the three known anomaly free theories with $G_1\times G_2 \times U(1)_R$ type symmetry, we find only six new remarkably anomaly free models with symmetry groups of the form $G_1\times G_2\times G_3 \times U(1)_R$. In the case of $n_T=1$ and ungauged models, excluding low rank group factors and considering only low lying representations, we find all anomaly free theories. Remarkably, the number of group factors does not exceed four in this class. The proof of completeness in this case relies on a bound which we establish for a parameter characterizing the difference between the number of non-singlet hypermultiplets and the dimension of the gauge group.

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