Motivated by recent numerical and experimental studies of the spin-1/2 Heisenberg antiferromagnet on the kagome lattice, we formulate a many-body model for fermionic spinons introduced by us earlier [ Phys. Rev. Lett. 103 187203 (2009)]. The spinons interact with an emergent U(1) gauge field and experience strong short-range attraction in the S=0 channel. The ground state of the model is generically a Z2 liquid. We calculate the edge of the two-spinon continuum and compare the theory to the slave-fermion approach to the Heisenberg model.