  SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which
describes planar curves which are statistically self-similar but not
conformally invariant in the strict sense. We show that, in the context of
boundary conformal field theory, this process arises naturally in models which
contain a conserved U(1) current density J, in which case it gives rise to a
highest weight state satisfying a deformation of the usual level 2 null state
condition.
  We apply this to a free field theory with piecewise constant Dirichlet
boundary conditions, with a discontinuity lambda at the origin, and argue that
this will lead to level lines in the bulk described by SLE(4,rho) across which
there is a universal macroscopic jump lambda* in the field, independent of the
value of lambda.
