On the geometrical interpretation of locality in anomaly cancellation

A notion of local section of the determinant line bundle is defined giving necessary and sufficient conditions for anomaly cancellation compatible with locality. This definition gives an intrinsic geometrical interpretation of the local counterterms allowed in the renormalization program of quantum field theory. For global anomalies the conditions for anomaly cancellation are expressed in terms of the equivariant holonomy of the Bismut-Freed connection.