  Within the framework of AdS/QCD models, the spectra of radially excited
hadrons are identified with towers of Kaluza-Klein (KK) states in a putative
dual theory. The infinite number of KK states is indispensable to provide
correct high energy asymptotics of correlation functions in QCD. It is known,
however, that the KK modes of dual theory must be qualitatively different from
real hadrons. And what is more important, the radially excited states appear in
lattice calculations not as "excitations" of some ground state, but rather as
independent states coupled to higher dimensional QCD operators - the larger is
a basis of interpolating operators, the larger set of states can be resolved. A
question arises whether it is possible to reconcile the holographic and lattice
descriptions of radially excited hadrons? We propose a new phenomenological
"consistency test" for bottom-up holographic models: If the KK spectrum of
massive 5D fields corresponding to higher dimensional operators in QCD
coincides with the conventional radial KK spectrum, then the holographic KK
states can be identified with real excited mesons in the large-Nc limit of QCD
- as in the lattice QCD, they become a superposition of several states
interpolated by operators of different canonical dimensions. We demonstrate
that the Soft Wall holographic model passes this test while the Hard Wall model
does not.
