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The original reference for the derivation of this result is http://arxiv.org/abs/hep-th/9302047. A brief answer to your questions is: the Euler density in generic number of dimensions is a diffeo-invariant functional of the metric, built out of the curvature. In dimension 2d it is a polynomial of degree d in the Riemann tensor. Its defining property ...

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A good analogy for the difference between the two can be given in terms of two other examples of anomalies, that are possibly more familiar. Consider a field theory with a global symmetry, take $U(1)$ for simplicity. At the classical level, the equations of motion lead to the existence of a conserved current (Noether's theorem). At the quantum level, the ...

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for an analysis of anomalies via quantum impedances, see http://vixra.org/author/peter_cameron the paper on the pizero, eta, and etaprime branching ratios gives another perspective

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