Open-Closed Correspondence of K-theory and Cobordism

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.

36 pages, 2 figures, 5 tables; v2: 35 pages, 1 figure, 5 tables, substantial revision of mainly section 5

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Cited by in corpus (6)

• Dynamical Cobordism of a Domain Wall and its Companion Defect 7-brane
• IIB Explored: Reflection 7-Branes
• Dimensional Reduction of Cobordism and K-theory
• Looking for structure in the cobordism conjecture
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Metastable vacua from torsion and machine learning