The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.
Cited by 1
Basile et al., Revisiting Dudas-Mourad Compactifications
Universe 8, 544 (2022) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Laboratoire d'Annecy-le-Vieux de Physique Théorique [LAPTh]
- 2 Universität Wien / University of Vienna
- 3 Max-Planck-Institut für Physik / Max Planck Institute for Physics [MPP]
- Alexander von Humboldt-Stiftung / Alexander von Humboldt Foundation
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]