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Gauge Field Localization in the Linear Dilaton Background

We study dynamical self-localization of gauge theories in higher dimensions. Specifically, we consider a 5D $U(1)$ gauge theory in the linear dilaton (clockwork) background, with anisotropic gauge couplings along the transverse (fifth) direction and the longitudinal (four-dimensional) directions. By using lattice techniques, we calculate the space plaquettes and the helicity moduli and we determine the phase diagram of the model. We find strong evidence that the model exhibits a new phase, a layer phase, where the four-dimensional physics decouples from the five-dimensional dynamics. The layer phase corresponds to a strong force along the fifth direction and a Coulomb phase along the four-dimensional longitudinal directions. This is in accordance with the clockwork mechanism where light particles with exponentially suppressed interactions are generated in theories with no fundamental small parameters.