Aspects of symmetries throughout the String Theory Moduli Space

This thesis aims to explore various corners of the string theory moduli spaces using symmetries as a guiding principle to uncover properties of the corresponding theories and their implications for spacetime dynamics. 

 Within the Swampland Program, the absence of global symmetries in consistent quantum gravity theories is a key principle, reformulated in string theory as the Cobordism Conjecture: any consistent configuration must admit spacetime boundaries, often realized by stringy defects that trivialize cobordism charges. The first part of this thesis implements this idea in effective field theory throughDynamical Cobordism solutions, where codimension-1 end-of-the-world (ETW) branes appear as finite-distance singularities with scalars diverging to infinite field space. These provide a framework to probe infinite-distance limits in the moduli/field space and Swampland constraints. We construct explicit examples with one or multiple scalars, including networks of intersecting ETW branes, and apply them to study infinite-distance singularities in Calabi–Yau fourfold moduli spaces, described via asymptotic Hodgetheory.

On the other hand, we turn to a microscopic approach to string theory and investigate worldsheet generalized symmetries, defined by topological operators with possibly non-invertible fusion rules. In particular, we analyze the category of topological defects commuting with spectral flow and N=(4,4) superconformal symmetry in K3 sigma models. Bystudying their fusion with boundary states, we argue that while certain models admit infinitely many, or even continuous families of defects, at generic points in the K3 moduli space the category is actually trivial.

Supervisor: Ángel Uranga