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

Na4Ir3O8 as a 3D spin liquid with fermionic spinons