论文标题
渐近线紧凑；时期，通量电势和滚动
Asymptotic String Compactifications; Periods, flux potentials, and the swampland
论文作者
论文摘要
在这篇论文中，我们研究了在弦弦压缩中渐近霍奇理论的各种应用。该数学框架捕获了产生的有效理论的物理耦合如何在内部卡拉比（Calabi-Yau）退化的情况下在田间空间边界附近的行为。在下面，我们总结了本论文分配的三个部分。 第一部分介绍了我们在本文中使用的渐近杂货理论的技术。我们回顾了Schmid的Nilpotent轨道定理的结果以及Cattani，Kaplan和Schmid的多变量SL（2）-Orbit定理。该讨论是针对弦乐紧凑型应用的应用，解释了如何描述重要的物理耦合，例如kähler电位和模量空间边界附近的磁通电位。 第二部分讨论了用于在渐近周期内构建一般模型的几何应用。以渐近hodge理论施加的限制为一致性原则，我们开发了构建这些时期的新方法。我们明确地针对所有可能的单一和两个模型边界执行我们的计划。 第三部分讨论了在弦弦压缩中渐近霍奇理论的两种应用。第一个研究弱重力猜想在4D $ \ MATHCAL {n} = 2 $ SuperGravity Theories的设置中提出的界限。第二个应用研究了复杂结构模量空间中渐近状态中的通量电位，我们开发了两个用于模量稳定的方案。第一个方案设置了一个近似程序，用于查找通量真空的三个步骤：SL（2） - Approximation，Nilpotent Orbit近似值和完全校正的结果。第二个方案通过使用由渐近hodge理论控制的必需指数校正来构建具有较小的通量超电势的通量真空。
In this thesis we have studied various applications of asymptotic Hodge theory in string compactifications. This mathematical framework captures how physical couplings of the resulting effective theories behave near field space boundaries where the internal Calabi-Yau manifold degenerates. Below we summarize the three parts in which this thesis is divided. Part I introduces the techniques from asymptotic Hodge theory we used throughout this thesis. We review the results of the nilpotent orbit theorem of Schmid and the multi-variable sl(2)-orbit theorem of Cattani, Kaplan and Schmid. This discussion is tailored to applications in string compactifications, explaining how to describe important physical couplings such as Kähler potentials and flux superpotentials near boundaries in moduli spaces. Part II discusses a geometrical application with the construction of general models for asymptotic periods. Taking the constraints imposed by asymptotic Hodge theory as consistency principles, we develop new methods for constructing these periods. We explicitly carry out our program for all possible one- and two-moduli boundaries. Part III discusses two applications of asymptotic Hodge theory in string compactifications. The first investigates bounds put by the Weak Gravity Conjecture in the setting of 4d $\mathcal{N}=2$ supergravity theories arising from Type IIB Calabi-Yau compactifications. The second application studies flux potentials in asymptotic regimes in complex structure moduli space, where we develop two schemes for moduli stabilization. The first scheme sets up an approximation procedure for finding flux vacua divided in three steps: the sl(2)-approximation, the nilpotent orbit approximation, and the fully corrected result. The second scheme constructs flux vacua with a small flux superpotential by using essential exponential corrections controlled by asymptotic Hodge theory.
