Open-closed correspondence of K-theory and cobordism

Abstract

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.