Chiral and gravitational anomalies in any dimension

Gravitational contributions to the chiral anomaly in 4<i>N</i> space‐time dimensions as well as the purely gravitational anomaly in 4<i>N</i>−2 dimensions are expressed in terms of the Riemann–Christoffel tensor. Using this formula, we give a simple proof that if <i>N</i>≥4 there is no way to cancel the gravitational anomalies using fields of spin‐ 1/2 , ‐ 3/2 , and ‐1.