  We study the quantum Ising antiferromagnet on the Kagome lattice, with weak
transverse field dynamics and other local perturbations. We analytically
demonstrate the possibility of a disordered zero-temperature phase that is
smoothly connected to the phase at strong transverse fields. This is done by
means of an appropriate mapping to a compact U(1) gauge theory on the honeycomb
lattice that is coupled to a charge-1 matter field. Our results are consistent
with existing Monte-Carlo calculations. The differences with other commonly
studied lattices (in which such disordered phases do not obtain at weak
transverse fields) is explained. Ordered phases are also shown to be possible
in principle in the weak transverse field limit, and are briefly studied.
