The Continuum Linear Dilaton

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.