nLab swampland cobordism conjecture -- references

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:

• 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:

• Ralph Blumenhagen, Nullifying Cobordism in Quantum Gravity, talk at QFT and Cobordism, CQTS (Mar 2023) $[$web$]$

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):

• Hisham Sati, Urs Schreiber, $\,$M/F-Theory as Mf-Theory (arXiv:2103.01877)