  We present a projective symmetry group (PSG) analysis of the spinless
excitations of Z2 spin liquids on the kagome lattice. In the simplest case,
vortices carrying Z2 magnetic flux ('visons') are shown to transform under the
48 element group GL(2, Z3). Alternative exchange couplings can also lead to a
second case with visons transforming under 288 element group GL(2, Z3) \times
D3. We study the quantum phase transition in which visons condense into
confining states with valence bond solid order. The critical field theories and
confining states are classified using the vison PSGs.
