Abstract
Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, which can be considered as the physical manifestation of a generalisation of the classic Conner-Floyd isomorphism. The picture is exemplified by the relations between KO-groups and Spin-cobordisms and between K-groups and Spinc-cobordisms. We suggest that global symmetries related by such an isomorphism are generically gauged. Indeed, by combining non-torsion K-theory and cobordism groups, we recover tadpole cancellation conditions well known from type I string theory and F-theory. For torsion charges, another possibility opens up.
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Blumenhagen, R., Cribiori, N. Open-closed correspondence of K-theory and cobordism. J. High Energ. Phys. 2022, 37 (2022). https://doi.org/10.1007/JHEP08(2022)037
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DOI: https://doi.org/10.1007/JHEP08(2022)037