  Within the bottom-up holographic approach to QCD, the highly excited hadrons
are identified with the bulk normal modes in the fifth "holographic" dimension.
We show that additional states in the same mass range can appear also from
taking into consideration the 5D fields dual to higher dimensional QCD
operators. The possible effects of these operators were not taken into account
in almost all phenomenological applications. Using the scalar case as the
simplest example, we demonstrate that the additional higher dimensional
operators lead to a large degeneracy of highly excited states in the Soft Wall
holographic model while in the Hard Wall holographic model, they result in a
proliferation of excited states. The considered model can be viewed as the
first analytical toy-model predicting a one-to-one mapping of the excited meson
states to definite QCD operators to which they prefer to couple.
