  Within the AdS/CFT correspondence, for description of $\mathcal{N}=4$ super
Yang-Mills theory in four dimensions one needs not only low-energy supergravity
on AdS$_5$ but also the whole infinite tower of massive Kaluza-Klein (KK)
states on AdS$_5\times$S$_5$ which appear after the KK-compactification on
five-dimensional sphere. The latter aspect is usually ignored in
phenomenological AdS/QCD models. The emerging massive 5D fields on AdS$_5$ are
dual to higher-dimensional operators in 4D gauge theory, with masses being
known polynomial functions of canonical dimensions of these operators.
Motivated by this observation, we propose to calculate the spectrum of radially
excited hadrons in bottom-up holographic QCD models as spectrum of zero KK
modes of massive 5D fields dual to higher dimensional operators in QCD. A
relevant physical motivation is suggested. The radial states with growing
masses are then enumerated by growing dimensions of interpolating QCD
operators. We tested the proposal in the Soft Wall and Hard Wall holographic
models in the sector of light mesons. The spectrum of Soft Wall model turns out
to be unchanged in the new description. But in the Hard Wall model, our
approach is shown to lead to a much better phenomenological spectrum of vector
radial excitations than the traditional description.
