  We show that there exists a long-range RVB state for the kagome lattice
spin-1/2 Heisenberg antiferromagnet for which the spinons have a massless Dirac
spectrum. By considering various perturbations of the RVB state which give mass
to the fermions by breaking a symmetry, we are able to describe a wide-ranging
class of known states on the kagome lattice, including spin-Peierls solid and
chiral spin liquid states. Using an RG treatment of fluctuations about the RVB
state, we propose yet a different symmetry breaking pattern and show how
collective excitations about this state account for the gapless singlet modes
seen experimentally and numerically. We make further comparison with numerics
for Chern numbers, dimer-dimer correlation functions, the triplet gap, and
other quantities. To accomplish these calculations, we propose a variant of the
SU(N) theory which enables us to include many of the effects of Gutzwiller
projection at the mean-field level.
