Looking for structure in the cobordism conjecture

Abstract

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.

41 pages; v2: minor changes

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• Heisenberg Groups and Noncommutative Fluxes
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• Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes
• Shedding black hole light on the emergent string conjecture
• Revisiting Dudas-Mourad compactifications
• Dimensional Reduction of Cobordism and K-theory
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Gravitational Background of Alice-Vortices and R7-Branes