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Topological Quantum Dark Matter via Standard Model's Global Gravitational Anomaly Cancellation
Abstract
symmetry is preserved as discrete finite subgroups rather than a continuous U(1), the perturbative
local anomalies become nonperturbative global anomalies. We systematically enumerate
these gauge-gravitational global anomalies involving discrete B ± L that are enhanced from the
fermion parity ZF2 to ZF2N , with N = 2, 3, 4, 6, 9, etc. The discreteness of B ± L is constrained by
multi-fermion deformations beyond-the-SM and the family number Nf . Unlike the free quadratic
νR Majorana mass gap preserving the minimal ZF2 , we explore novel scenarios canceling (B ± L)-gravitational anomalies
of the family number at Nf = 3, such that when the representation of ZF2N from the faithful B + L
for baryons at N = Nf = 3 is extended to the faithful Q + NcL for quarks at N = NcNf = 9, this
symmetry extension ZNc=3 → ZNcNf =9 → ZNf =3 matches with the topological order dark matter
construction. Key implications include: (1) a 5th force mediating between SM and dark matter via
discrete B±L gauge fields, (2) dark matter as topological order quantum matter with gapped anyon
excitations at ends of extended defects, and (3) Ultra Unification and topological leptogenesis.