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We study the kagome antiferromagnet for quantum spin-1/2 with first J1,second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We useSchwinger-boson mean-field theory for the precise determination of the phasediagram, and two different rewritings of the Hamiltonian to build an intuitionabout the origin of the transitions. The spin liquid obtained at J = 0 remainsessentially stable over a large window, up to J = 1/3, because it is onlyweakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spinliquid condenses into a long-range chiral order because of the change of natureof local magnetic fluctuations. As a side benefit, our Hamiltonian rewritingoffers an exact solution for the ground state of our model on a Husimi cactus.

Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet