\_ł[14]{} D\_[-ø]{}()\_[”=,]{}&lt;\_[”,-ø,]{}\^-\_[’,ø’,]{}\^+\_[’,ø’,+]{}&gt;\_[T, 0,N]{}+R\_[N,]{}(,)\[aaaa7\] with \_=-1,\_=1\[aaadd\] and $R_{N,\a}(\kk,\pp)$ is in absolute value smaller than ${
2^{-N}\over |\kk||\kk-\pp|}$, that is vanishing for $N\to\io$.

If we restrict to the fermionic sector, in the limit $N\to\io$ the first term in the r.h.s. of (32) would be the chiral anomaly and the second term is vanishing. The fact that the chiral anomaly is [*linear*]{} in the coupling is a property called Adler-Bardeen theorem. It is important to stress the presence of the correction term $R_N$ in the l.h.s. of (32), which is vanishing [*only*]{} in the $N\to\io$ limit. The derivation of (32) is based on a multiscale integration also for the correction term in , and the main difference is that the source term $(J_\xx,\Psi^+_{\xx}\Psi_\xx)$ is replaced by $\int d\xx \chi_{\a,\o}\d\r_{\a,\o,\xx}$ where $\chi$ is a source term. After the integration of the fields $\Psi^{(N)},\Psi^{(N-1)},..,\Psi^{(h+1)}$ the effective potential can be again written as sum of monomials with $n$ $\Psi$ fields, and $m$ $\chi$ fields with kernels $\tilde W^{(h)}_{n,m}$. The analysis of $\tilde W^{(h)}_{2,1}$ is very similar to the analysis of $W^{(h)}_{2,1}$ in the previous section. An important difference with respect to the bound comes from the fact that $C_{N}(\kk,\pp)
g^{(i)}(\kk)g^{(j)}(\kk+\pp)$ vanishes unless either $i$ or $j$ 