  Spin liquid states for spin-1/2 antiferromagnetic Heisenberg model on a
hyperkagome lattice are studied. We classify and study flux states according to
symmetries. Applying this model to Na4Ir3O8, we propose that the high
temperature state may be described by a spinon Fermi surface, which forms a
paired state with line nodes below 20 K. The possible mixed spin singlet and
spin triplet pairing states are discussed according to the lattice symmetry
which breaks inversion.

Strongly Correlated Electrons