AI 中文总结
该论文研究4维带通量F-理论紧致化，提出利用垂直与剩余通量破缺刚性规范群的方法，构造含高电荷阿贝尔规范对称性的模型，提出基于E₇的新大统一理论。
AI 中文摘要
本论文研究带通量的4维F-理论紧致化及其与粒子物理的关联，同时对F-理论进行综述。首先，我们建立了利用通量实现规范对称性破缺的一般形式体系：垂直通量与剩余通量可用于破缺刚性规范群，前者还能同时诱导手征物质，即便未破缺的规范群无复表示；我们发现存在三代手征物质的可能性很大。我们聚焦于通过中间SU(5)规范群破缺刚性E₇、E₆规范群以实现标准模型规范群与手征物质的过程，并提供了具体构造的示例。随后，我们详细研究了刚性E₇模型的唯象学方面，发现诸多类标准模型特征可自然与E₇模型兼容，例如4维和5维质子衰变普遍受到抑制，这些特征多源于E₇的群论结构及其F-理论几何；特别地，一组近似整体对称性从E₇群导出，导致非期望耦合呈指数级抑制，这些特征提出了基于E₇群及其弦论构造的新系列大统一理论。最后，我们研究带奇异电荷的阿贝尔规范对称性构造：通过垂直通量将刚性非阿贝尔群破缺为U(1)规范群，无质量或轻谱中可出现极大电荷；我们在4维F-理论中给出了具体构造，其中矢量样物质携带的电荷高达657，远高于此前F-理论中的已知上限；我们定性论证该结果可能为F-理论景观中退耦U(1)规范群下轻场的电荷提供上限。
英文摘要
This thesis studies 4D F-theory compactifications with fluxes and their connection to particle physics, accompanied with a review of F-theory. First, we develop a general formalism for gauge symmetry breaking with fluxes. Vertical and remainder fluxes can be used to break a rigid gauge group, with the former simultaneously inducing chiral matter, even when the unbroken gauge group has no complex representations. We show that it is fairly likely to have three generations of chiral matter. We focus on the realization of the Standard Model gauge groups and chiral matter by breaking rigid $E_7,E_6$ gauge groups with an intermediate SU(5) gauge group, and provide examples of explicit constructions. Then, the phenomenological aspects of rigid $E_7$ models are studied in detail. We find that many other Standard-Model like features are naturally compatible with the $E_7$ models. For example, dimension-4 and dimension-5 proton decay are ubiquitously suppressed. Many of these features are due to the group-theoretic structure of $E_7$ and its F-theory geometry. In particular, a set of approximate global symmetries descends from the $E_7$ group, leading to exponential suppression of undesired couplings. These features suggest a new set of grand unified theories based on the $E_7$ group and its string theory construction. Finally, we study constructions of abelian gauge symmetries with exotic charges. By breaking a rigid nonabelian group to a U(1) gauge group using vertical flux, very large charges can arise in the massless or light spectrum. We give an explicit construction in 4D F-theory in which the vector-like matter carries charges as large as 657, which is much larger than the previously known bounds in F-theory. We heuristically argue that this result may provide an upper bound on charges for light fields under decoupled U(1) gauge groups in the F-theory landscape.
CommentsPhD thesis; 189 pages, 3 figures
