Categorical Symmetry of the Standard Model from Gravitational Anomaly

Understand

In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf L$ number symmetry is free of mixed anomalies with strong and electroweak $su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces.

• However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent to leptogenesis in the very early universe.
• This happens when the total "sterile right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number $N_f$.
• Thus the invertible $\bf B - L$ symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons.