  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.
