标题： 弦真空的稳定性、刚性和幺正性方面 显示英文标题

标题： Aspects of Stability, Rigidity and Unitarity in String Vacua

摘要： 本论文研究了十维及更低维度弦景观的稳定性、刚性和幺正性性质。 论文通过将具有和不具有超对称性的弦真空的详细分析与由幺正性驱动的自下而上的研究交织在一起，探索了这些方面。 特别是，在第一章讨论了为非超对称弦真空的经典稳定性制定必要且充分条件的可能性，并强调了十维和九维的例子。 在第二章中，对于BSB和具有超对称性的$T^4/\mathbb{Z}_6$向量量规真空解，在六维中提出了一些新的解，这些解源于R-R蝌蚪项的非平凡抵消。 通过检查局部异常的抵消并验证引入弦缺陷后产生的幺正约束，证明了这些理论的一致性。 最后，第三章讨论了一种新型全局异常的作用，该异常源于有效场论在拓扑变化中的不一致性。 讨论了具有$\text{SU}(2)$规范群和一个张量超多重态以及$\text{U}(1)$规范群且没有张量多重态的六维超引力理论的系统分析。 发现了新的约束条件，并验证了它们在弦真空中的抵消。 此外，我们还研究了$\text{SO}(16)\times \text{SO}(16)$异质理论在$T^4/\mathbb{Z}_6$奥尔比福德上的紧化以及没有张量多重态的Gepner向量量规，展示了如何抵消这些异常。 尽管可以预期，但这一结果提供了非平凡的一致性检查，这是文献中已知的任何定理都无法保证的。 显示英文摘要

摘要： In this Thesis we investigate properties of stability, rigidity and unitarity of the string landscape in ten and lower dimensions. The dissertation explores these aspects by intertwining a detailed analysis of string vacua, with and without supersymmetry, with a bottom-up study driven by unitarity. In particular, in Chapter 1 the possibility of formulating a necessary and sufficient condition for the classical stability of non-supersymmetric string vacua is discussed, emphasising the examples in ten and nine dimensions. In Chapter 2, new solutions are presented in six dimensions both for BSB and supersymmetric $T^4/\mathbb{Z}_6$ orientifold vacua, arising from a non-trivial cancellation of the R-R tadpoles. The consitency of these theories is shown by checking the cancellation of local anomalies and verifying the unitarity constraints arising from the introduction of string defects. Finally, Chapter 3 discusses the role played by a new kind of global anomaly, arising from the inconsistency of effective field theories under topology change. A systematic analysis of six-dimensional supergravity theories with $\text{SU}(2)$ gauge group and one tensor multiplet and $\text{U}(1)$ gauge group with no tensor multiplets is discussed. Novel constraints are found and their cancellation in string vacua is verified. In addition, we have investigated the $\text{SO}(16)\times \text{SO}(16)$ heterotic theory compactified on the $T^4/\mathbb{Z}_6$ orbifold and the Gepner orientifold with no tensor multiples, showing how such anomalies are cancelled. Even though expected, this result provides a non-trivial consistency check that is not guaranteed by any theorem known in the literature.