  We study Fermi-Hubbard models with kinetically constrained dynamics that
conserves both total particle number and total center of mass, a situation that
arises when interacting fermions are placed in strongly tilted optical
lattices. Through a combination of analytics and numerics, we show how the
kinetic constraints stabilize an exotic non-Fermi liquid phase described by
fermions coupled to a gapless bosonic field, which in many respects mimics a
dynamical gauge field. This offers a novel route towards the study of non-Fermi
liquid phases in the precision environments afforded by ultracold atom
platforms.
