Aspects of Stability, Rigidity and Unitarity in String Vacua

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.