  We use a slave-rotor approach within a mean-field theory to study the
competition of metallic, Mott-insulating, and superconducting phases of
spin-3/2 fermions subjected to a periodic optical lattice potential. In
addition to the metallic, the Mott-insulating, and the superconducting phases
that are associated with the gauge symmetry breaking of the spinon field, we
identify a novel emerging superconducting phase that breaks both roton and
spinon field gauge symmetries. This novel superconducting phase emerges as a
result of the competition between spin-0 singlet and spin-2 quintet interaction
channels naturally available for spin-3/2 systems. The two superconducting
phases can be distinguished from each other by quasiparticle weight. We further
discuss the properties of these phases for both two-dimensional square and
three-dimensional cubic lattices at zero and finite temperatures.
