World-sheet dynamics of EFT strings

String theory allows for huge classes of possible models admitting a gravitational low-energy effective description. However, not any effective field theory (EFT) of gravity admits a string theory UV completion. By using string theory as the main theoretical laboratory, the “Swampland program” aims at identifying the hallmarks distinguishing the “landscape” of gravitational EFTs that admit a consistent UV completion from the “swampland” of seemingly consistent EFTs that do not. In this context, it has been recently realized that the perturbative regimes of UV complete four-dimensional N=1 (i.e. minimally supersymmetric) EFTs are strongly characterized by the presence of specific types of fundamental strings, called EFT strings. The latter generically support an 'internal' world-sheet sector, besides the universal 'center of mass' sector, and it is currently unknown how to couple it to the bulk supergravity sector in a supersymmetrically controlled way. In this thesis, we illustrate how the universal sector of EFT strings can be coupled to four-dimensional N=1 supergravities by appropriately generalizing the superembedding formulation of superstrings. This provides a promising starting point to add the internal world-sheet sector. In this respect, we first study in depth the N=(0,2) two-dimensional supergravity. We finally give a first example of inclusion of the internal sector, considering N=(0,2) Fermi multiplets and N=(0,2) chiral multiplets. In the latter case, we show that a generalization of the superembedding condition is needed, leaving the investigation of this interesting aspect for future work.