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arXiv · 2208.01656

Dimensional Reduction of Cobordism and K-theory

Ralph Blumenhagen·Niccolò Cribiori·Christian Kneissl·Andriana Makridou
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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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Ralph Blumenhagen, Niccolò Cribiori, Christian Kneissl, Andriana Makridou. 2022-08-02. Dimensional Reduction of Cobordism and K-theory. https://doi.org/10.1007/jhep03(2023)181

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