Open-Closed Correspondence of K-theory and Cobordism

Ralph Blumenhagen; Niccolò Cribiori

doi:10.1007/jhep08(2022)037

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arXiv · 2112.07678

Open-Closed Correspondence of K-theory and Cobordism

Ralph Blumenhagen·Niccolò Cribiori

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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 Spin$^c$-cobordisms. Global symmetries related by such isomorphism are eventually gauged. By combining K-theory and cobordism, we recover then tadpole cancellation conditions in type I string theory and F-theory from a bottom-up perspective.

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BibTeX RIS

Ralph Blumenhagen, Niccolò Cribiori. 2021-12-14. Open-Closed Correspondence of K-theory and Cobordism. https://doi.org/10.1007/jhep08(2022)037

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