Analysis of anomalies in higher space-time dimensions

The anomaly for a dimension $D=2n$ gauge theory is calculated for arbitrary $n\ge 2$ from the $l$-agon Feynman diagram with $l=(n+1\mathrm{})\mathrm{}$. The result is both finite and unique despite the nonrenormalizability of the theory. The contributions of higher polygons to the anomaly are deduced from gauge invariance and Lorentz invariance. The no-anomaly condition in $D=2n$ is the vanishing of a symmetrized trace over $l$ generators written in the fermion representation. It is shown how to compute this trace for totally antisymmetric representations of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$.