SLE(kappa,rho) and Conformal Field Theory
Abstract
Description
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.
18 pages, 1 figure. v.2: section about kappa not equal to 4 deleted
18 pages, 1 figure. v.2: section about kappa not equal to 4 deleted