nLab swampland cobordism conjecture -- references

Swampland cobordism conjecture

Swampland cobordism conjecture

The swampland cobordism conjecture is the hypothesis that consistency of vacua in string theory/M-theory/F-theory (hence their being in the “landscape” instead of the “swampland”) requires (undefined) stringy/quantum gravity-analogs of cobordism groups to vanish:

Relation to topological K-theory and D-brane charge quantization in K-theory:


A more concrete consequence of this conjecture is claimed (McNamara & Vafa 2019, Sec. 5.2, 2nd paragr.) to be the statement that – paraphrasing/extrapolating somewhat (in line with Blumenhagen & Cribiori 2022; Blumenhagen et al. 2023; Blumenhagen 2023, p. 23): Certain topological brane charges are quantized in Cobordism cohomology; so that, in particular tadpole cancellation of brane charges is to happen in Cobordism cohomology. This kind of statement is also discussed, as a consequence of Hypothesis H, in (see p. 83):

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