We study S=1 spin liquid states on the kagome lattice constructed by
Gutzwiller-projected px​+ipy​ superconductors. We show that the obtained spin
liquids are either non-Abelian or Abelian topological phases, depending on the
topology of the fermionic mean-field state. By calculating the modular matrices
S and T, we confirm that projected topological superconductors are
non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin
Hall conductance we obtained agree very well with the SO(3)1​ (or,
equivalently, SU(2)2​) field theory predictions. We propose a local
Hamiltonian which may stabilize the NACSL. From a variational study we observe
a topological phase transition from the NACSL to the Z2​ Abelian spin liquid.Comment: 12 pages, 7 figures, 1 tabl