  We apply ideas from conformal field theory to study symplectic
four-manifolds, by using modular functors to "linearise" Lefschetz fibrations.
In Chern-Simons theory this leads to the study of parabolic vector bundles of
conformal blocks. Motivated by the Hard Lefschetz theorem, we show the bundles
of SU(2) conformal blocks associated to Kaehler surfaces are Brill-Noether
special, although the associated flat connexions may be irreducible if the
surface is simply-connected and not spin.
