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Leaving out numerical factors, we have that $$ \mathrm{d}j_A = \mathrm{Tr}(F \wedge F)$$ This already shows that we are dealing with a topological quantity, since the RHS is the second Chern character of the gauge field (or rather, the principal bundle associated to it). Now, there is also the (3D) Chern-Simons form $$ \omega = \mathrm{Tr}(F \wedge A - ...


We should distinguish between the different types of anomalies that can arise in quantum field theory. An anomaly is a symmetry of the classical action that is not preserved in the quantum theory. A gauge anomaly causes a gauge symmetry to be broken leading to a violation of a Ward identity which is needed to ensure that unphysical polarization states and ...

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