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:
Jacob McNamara, Cumrun Vafa, Cobordism Classes and the Swampland (arXiv:1909.10355, spire:1755441)
Miguel Montero, Cumrun Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle, J. High Energ. Phys. 2021, 63 (2021) (arXiv:2008.11729)
Markus Dierigl, Jonathan Heckman, On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups, Physical Review D 2021 (arXiv:2012.00013)
Hirosi Ooguri, Tadashi Takayanagi, Cobordism Conjecture in AdS (arXiv:2006.13953)
David Andriot, Nils Carqueville, Niccolò Cribiori, Looking for structure in the cobordism conjecture (arXiv:2204.00021)
Relation to topological K-theory:
Ralph Blumenhagen, Niccolò Cribiori, Christian Kneissl, Andriana Makridou, Dimensional Reduction of Cobordism and K-theory $[$arXiv:2208.01656$]$
Ralph Blumenhagen, Christian Kneissl, Chuying Wang, Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes $[$arXiv:2303.03423$]$
Review:
A more concrete consequence of this conjecture is claimed (McNamara-Vafa 17, Sec. 5.2, 2nd paragr.) to be the statement that – paraphrasing/extrapolating somewhat: brane charges are quantized in Cobordism cohomology; so that, in particular tadpole cancellation of brane charges is to happen in Cobordism cohomology. This statement is discussed, as a consequence of Hypothesis H, in (see p. 83):
Last revised on March 18, 2023 at 09:27:14. See the history of this page for a list of all contributions to it.