Dimensional Reduction of Cobordism and K-theory

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.

55 pages + appendices, v2: major modifications in sec. 4.3, published version

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Cited by in corpus (7)

• Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes
• Emergence of Species Scale Black Hole Horizons
• Shedding black hole light on the emergent string conjecture
• IIB Explored: Reflection 7-Branes
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Gravitational Background of Alice-Vortices and R7-Branes
• Open Strings and Heterotic Instantons