We study the kagome antiferromagnet for quantum spin-1/2 with first $J_1$, second $J_2$, and third $J_3$ neighbor exchanges, along the $J_2=J_3\equiv J$ line. We use Schwinger boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at $J=0$ remains essentially stable over a large window, up to $J\approx 1/3$, because it is only weakly frustrated by the $J$ term. Then, at $J\approx 1/2$, the intermediate $Z_2$ spin liquid condenses into a long-range chiral order because of the change of nature of the local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.

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• Frustrated magnetism
• Quantum spin liquid
• Schwinger boson method