Using the Fujikawa and the heat-kernel methods we make a complete and detailed computation of the global, gauge, and gravitational anomalies in the standard model defined on a curved space-time with torsion. We find new contributions coming from the curvature and the torsion to the leptonic number anomaly (so that $B-L$ is not conserved anymore) to the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$ gauge and to the mixed $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$-gravitational anomalies. However, neither gauge nor gravitational new anomaly cancellation conditions for the hypercharges arise.

• Received 4 August 1995

DOI:https://doi.org/10.1103/PhysRevD.54.5185