Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
Invertible phases of matter with spatial symmetry
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a crystallographic group, the term `topological crystalline phases' is sometimes used for these phases of matter.
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Computes E2 pages of momentum- and real-space AHSS for 1651 magnetic space groups and determines compatible K-groups for ~59% of 3D symmetry settings under a physical assumption.
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Anomalies in family unification models from bordism classification
Family unification models from E7 cosets have no global sigma model anomalies because the torsion parts of their bordism groups vanish, as computed via the Atiyah-Hirzebruch spectral sequence, including when isotropy subgroups are gauged.
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Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
Computes E2 pages of momentum- and real-space AHSS for 1651 magnetic space groups and determines compatible K-groups for ~59% of 3D symmetry settings under a physical assumption.