Abstract
It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any consistent theory of quantum gravity, in accordance with swampland conjectures. We provide further support to this idea by showing that cobordism and K-theory groups of a general manifold X reproduce the pattern of symmetries expected from the dimensional reduction of the theory on X, as well as their breaking and gauging. To this end, we employ the Atiyah-Hirzebruch spectral sequence to compute such groups for common choices of X in string compactifications.
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Blumenhagen, R., Cribiori, N., Kneißl, C. et al. Dimensional Reduction of Cobordism and K-theory. J. High Energ. Phys. 2023, 181 (2023). https://doi.org/10.1007/JHEP03(2023)181
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DOI: https://doi.org/10.1007/JHEP03(2023)181