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, SciPost Phys. 13 (2022) 071 [arXiv:2204.00021, doi:10.21468/SciPostPhys.13.3.071]
Ralph Blumenhagen, Christian Kneissl, Chuying Wang, Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes, J. High Energ. Phys.2023 (2023) 123 [arXiv:2303.03423, doi:10.1007/JHEP05(2023)123]
Relation to topological K-theory and D-brane charge quantization in K-theory:
Ralph Blumenhagen, Niccolò Cribiori, Open-Closed Correspondence of K-theory and Cobordism, J. High Energ. Phys. 2022 37 (2022) [arXiv:2112.07678, doi:10.1007/JHEP08(2022)037]
Ralph Blumenhagen, Niccolò Cribiori, Christian Kneissl, Andriana Makridou, Dimensional Reduction of Cobordism and K-theory, Journal of High Energy Physics 2023, 181, [doi:10.1007/JHEP03(2023)181, arXiv:2208.01656]
Review:
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):
Last revised on March 29, 2024 at 22:10:19. See the history of this page for a list of all contributions to it.