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Anomalous part of baryon current in chiral effective field theory

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Let's assume QCD at high energies. It has $SU_{L}(3)\times SU_{R}(3)$ global symmetry. At $\Lambda_{\text{QCD}}$ scale this group is spontaneously broken to $SU_{f}(3)$. We can then extract Goldstone degrees of freedom from quark fields, $q \to Uq$, and replace $\bar{q}q$ term by vacuum expectation value. We will get chiral effective field theory in terms of $U$.

It can be shown that baryon current anomaly piece can be given in terms of $U$ as
$$
J^{\mu} = \frac{\epsilon^{\mu\nu\alpha\beta}}{24 \pi^{2}}\text{Tr}\left[U^{-1}\partial_{\nu}UU^{-1}\partial_{\alpha}UU^{-1}\partial_{\beta}U\right]
$$
How to derive this result?

asked Oct 7, 2015 in Theoretical Physics by NAME_XXX (1,010 points) [ revision history ]
edited Oct 7, 2015 by NAME_XXX

How do you know that the formula is valid?

It is represented in Witten's article (Eq. (2)), the reference of which you've given in your answer on my question about baryons as skyrmion solution.

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