We can describe the growth of a simply connected set in the plane by
thinking about how the conformal transformation, which maps it to some
standard set like the unit circle, evolves. For the scaling limit of sets
which arise 2d statistical mechanics (for example spin clusters in the
Ising model), this is conjectured to be particularly simple, and is
called Schramm-Loewner Evolution (SLE). However the scaling limit of such
models is also supposed to be described by conformal field theory (CFT).
We show that a link between these two can be made through so-called
parafermionic holomorphic observables, which can already be identified on
the lattice.
