4D F理论模型中的手性物质多重性和与分辨无关的结构
Chiral matter multiplicities and resolution-independent structure in 4D F-theory models
摘要：
受通量紧致化景观相关问题的启发，我们将新的和现有的技术结合成一个系统的，简化的方法，用于计算4D F理论模型中的垂直通量和手性物质多重性。我们的方法的一个中心特征是光滑椭圆CY四重的整数中间上同调的垂直部分的与分辨率无关的交叉配对，与计算手征指数和4D F-理论通量真空的相关方面有关。我们说明我们的方法通过分析垂直通量背景的F理论模型与简单，简单的花边规范群和一般的物质含量，以及模型与U（1）规范因子。我们明确地分析了这些F理论模型的分辨率，其中椭圆光纤在$\mathbb P^2$中实现为任意（例如，不一定是复曲面）光滑基，并确认了中间上同调的垂直部分的相交配对的分辨率无关性。在我们研究的每个模型中，我们发现，垂直通量背景可以产生非零的多重性为所有的无异常手性物质场的组合，这表明F-理论几何形状不施加额外的线性约束，超出了那些暗示的异常取消。
英文摘要：
Motivated by questions related to the landscape of flux compactifications, we combine new and existing techniques into a systematic, streamlined approach for computing vertical fluxes and chiral matter multiplicities in 4D F-theory models. A central feature of our approach is the conjecturally resolution-independent intersection pairing of the vertical part of the integer middle cohomology of smooth elliptic CY fourfolds, relevant for computing chiral indices and related aspects of 4D F-theory flux vacua. We illustrate our approach by analyzing vertical flux backgrounds for F-theory models with simple, simply-laced gauge groups and generic matter content, as well as models with U(1) gauge factors. We explicitly analyze resolutions of these F-theory models in which the elliptic fiber is realized as a cubic in $\mathbb P^2$ over an arbitrary (e.g., not necessarily toric) smooth base, and confirm the resolution-independence of the intersection pairing of the vertical part of the middle cohomology. In each model we study, we find that vertical flux backgrounds can produce nonzero multiplicities for all anomaly-free chiral matter field combinations, suggesting that F-theory geometry imposes no additional linear constraints beyond those implied by anomaly cancellation.
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