The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on  the star superlattice by Contractor Renormalization.

Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies  truncation of effective interactions at range 3. 

Within our accuracy,  magnetic and translational symmetries are not broken (i.e. a spin liquid ground state).  However, we discover

doublet spectral degeneracies which signal the onset of  p6 - chirality symmetry breaking.This is understood by simple mean field analysis.

Experimentally, the p6 chiral order parameter should split the optical phonon  degeneracy near the zone center.

Addition of weak next to nearest neighbor coupling is discussed