Quantum spin liquids are interacting spin systems characterized by the absence of long-range magnetic order even at zero temperature. I will talk about an example of a spin liquid that is chiral (i.e. breaks parity and time reversal symmetry) and whose excitations are Majorana fermions coupled to a Z_2 gauge field. We show that the spectrum is gapless along lines in the three-dimensional Brillouin zone, and that these nodal lines are topological defects (vortices) of a non-Abelian Berry connection. This work is motivated by recent experiments in Mott-insulating double perovskites with strong spin-orbit coupling.
