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Properties of WZ terms
(i)are metric independent (ii) are imaginary in Euclidian formulation (iii) do not contribute to stress-energy tensor (and to Hamiltonian). (iv) do not depend on m – the scale, below which an effective action is valid (but do depend on sgn (m)) (v) are antisymmetric in derivatives with respect to different space-time coordinates (contain !µνλ…) (vi) are written as integrals of (D+1)-forms over auxiliary (D+1)-dimensional space - disk $D^{D+1}$ such that ∂$D^{D+1}$ = $S^D$ - compactified space-time (vii) are multi-valued functionals. Multi-valuedness results in quantization of coupling constants (coefficients in front of WZ terms) (viii) do change equations of motion by changing commutation relation between fields (Poisson’s brackets) not by changing Hamiltonian (ix) might lead to massless excitations with “half-integer spin” (x) describe boundary theories of models with θ-terms (xi) being combined (see the spin chains chapter) produce θ-terms (xii) can be calculated by gradient expansion of the variation of fermionic determinants (xiii) produce θ terms as a reduction of target spaceAmong the listed properties the first five (i)-(v) are the properties of all topological terms while the others are more specific to WZ terms.
The chiral anomaly can be corrected by adding a Wess-Zumino term to the Lagrangian, but this term is not perturbatively renormalizable, thus does not solve the nonrenormalizability problem. https://physics.stackexchange.com/a/34022/37286