  In the top-down holographic model of QCD based on D4/D8-branes in type IIA
string theory and some of the bottom up models, the low energy effective theory
of mesons is described by a 5 dimensional Yang-Mills-Chern-Simons theory in a
certain curved background with two boundaries. The 5 dimensional Chern-Simons
term plays a crucial role to reproduce the correct chiral anomaly in 4
dimensional massless QCD. However, there are some subtle ambiguities in the
definition of the Chern-Simons term for the cases with topologically
non-trivial gauge bundles, which include the configurations with baryons. In
particular, for the cases with three flavors, it was pointed out by Hata and
Murata that the naive Chern-Simons term does not lead to an important
constraint on the baryon spectrum, which is needed to pick out the correct
baryon spectrum observed in nature. In this paper, we propose a formulation of
well-defined Chern-Simons term which can be used for the cases with baryons,
and show that it recovers the correct baryon constraint as well as the chiral
anomaly in QCD.
