Topological Quantum Dark Matter via Standard Model's Global Gravitational Anomaly Cancellation

In this talk, we propose that topological order can replace sterile neutrinos as dark matter candidates 

to cancel the Standard Model’s global gravitational anomalies. Standard Model (SM) with 15 Weyl fermions per family 

(lacking the 16th, the sterile right-handed neutrino νR) suffers from mixed gauge-gravitational anomalies tied to baryon number plus or minus

lepton number B±L symmetry. Including νR per family can cancel these anomalies, but when B±L
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 

while preserving the ZF2N discrete symmetries, featuring 4-dimensional interacting gapped topological orders 

or gapless sectors (e.g., conformal field theories). We propose symmetric anomalous sectors as 

quantum dark matter to cancel SM’s global anomalies. We find the uniqueness
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.