  Continuum spectra can be a way out to alleviate the tension generated by the
elusiveness of narrow resonances of new physics in direct experimental
searches. Motivated by the latter, we consider the linear dilaton model with a
continuum spectrum of KK modes. It is provided by a critical exponential bulk
potential for the scalar field stabilizing the distance, between the UV
boundary at $y=0$ and a naked (good) singularity at $y=y_s$, in proper
coordinates, which corresponds in conformal coordinates to $z_s\to\infty$. The
cutoff $M_s$ in this theory is an intermediate scale $M_s\simeq 10^{-5}M_{\rm
Pl}$ and the warped factor solves the hierarchy between $M_s$ and the TeV,
while the hierarchy between $M_{\rm Pl}$ and $M_s$ has to be solved by a
(Little) String Theory with coupling $g_s\simeq 10^{-5}$. The Standard Model is
localized on a 4D IR brane. The graviton and radion Green's and spectral
functions have a continuum of states with a TeV mass gap, and isolated poles
consisting on the 4D graviton and the light radion/dilaton. We construct the
effective field theory below the mass gap where the continua of KK modes are
integrated out, generating a set of dimension eight operators which contribute
to low energy electroweak precision observables, and high energy violation of
unitarity in vector boson scattering processes. The radion mass depends on the
stabilizing UV brane potential and its wave function is localized toward the IR
which enhances its coupling with the SM fields.
