Anomalies of QCD I have come across the following statement: 

The anomalies of QCD cannot be reproduced by a collection of free fermions
  carrying $U(1)_V$, $SU(N_f)_L$ and $SU(N_f)_R$ quantum numbers. That is why one must either have a CFT or a spontaneous symmetry breaking with massless bosons
  and Wess-Zumino-Witten terms.

I do not understand this statement. Can somebody elaborate this statement and recommend a good reference about it? I appreciate the help.
 A: The statement is relatively simple. The pure QCD has the so-called internal anomalies - the non-zero coefficients 
$$
\tag 1 D_{abc} = \text{tr}\left[ [t_{a},t_{b}]_{+}t_{c}\right]
$$ 
for the triangle diagram with running inside currents of the QCD global group 
$$
G\simeq SU_{L}(3)\times SU_{R}(3)\times U_{B}(1),
$$ 
with $a,b,c$ corresponding to the generators of $G$. Although there are no gauge fields associated to these currents, these coefficients must be reproduced at any scale of the theory. This statement is called the anomaly matching, and firstly it was discovered by 't Hooft. In particular it means that if below some scale a degree of freedom making the contribution into $(1)$ die out, then below this scale there must be new degrees of freedom making exactly the same contribution as the died one. For the QCD with its confinement, this means that
$$
\tag 2 D_{abc}\bigg|_{quarks} = D_{abc}\bigg|_{\text{quark bound states}},
$$
where the quark bound states belong to some representation of $G$.
In general, it is hard to calculate the right hand-side of $(2)$. Fortunately, there is non-trivial statement that the contribution into $D_{abc}$ can come only from massless degrees of freedom (or from particles whose mass directly violates the given generator symmetry). Spin-3/2 and higher degrees of freedom are forbidden because of the Lorentz covariance (the statement is known as Weinberg-Witten no-go theorem), the similar statement is true about the spin-1 degrees of freedom, so the only possible candidates are massless fermions and massless spin-zero particles. The latter are typically associated with the spontaneous symmetry breaking and then are called the Goldstone bosons. Therefore, the anomaly matching tells us that 

either in the QCD there are massless spin $1/2$ bound states
  reproducing $(1)$, or there is the SSB with the Goldstone bosons reproducing $(1)$.

For the QCD it was found that, assuming first existence of massless bound fermions, it is impossible to construct their representations which match $(2)$. Contrary, there is possible to construct an effective action composed from the Goldstone bosons which matches $(2)$. This action is called the Wess-Zumino-Witten action.
As for the resource I would recommend you Weinberg's QFT, Volume 2, 22.5. 
