Anomaly and Cobordism Constraints Beyond Standard Model: Topological Force

摘要: Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled chiral fermions, e.g. Models (SM). Based on a systematic cobordism classification [1812.11967, 1910.14668], we examine constraints from invertible quantum (including all perturbative and nonperturbative global anomalies) for theories. We also clarify different these anomalies: including (1) anomaly cancellations dynamical fields, (2) 't Hooft matching conditions background fields symmetries, others. find several 4d $\mathbb{Z}_{n}$ $n=16,4,2$, beyond familiar $\mathbb{Z}$ class Feynman graphs, Witten SU(2) new anomalies. As an application, (SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_6$ SM with 15n Weyl fermions (e.g. SU(5) Grand Unification) discrete $X=5(B-L)-4Y$ preserved, discover hidden sector previously unknown Georgi-Glashow model -- by appending known nearly gapless sector, propose strongly-correlated gapped Topological Mass mechanism: either non-invertible non-abelian topological field theory (TQFT) at low energy but heavy anyon excitations 1d particle worldline 2d string worldsheet gravity (accessible neither Dirac nor Majorana mass gap 16th fermions: 3 generations right-handed neutrinos, dual fermionic vortex zero mode bound state condensation via phase transition or duality/"mirror symmetry") 5d TQFT in extra dimensions. Above higher scale, $X$ becomes gauged, entangled Universe is mediated Force. Our resolves puzzles, surmounting sterile neutrinos dark matter, fundamental physics.