SLE(kappa,rho) and Conformal Field Theory

Details SLE(kappa,rho) and Conformal Field Theory SLE(kappa,rho) and Conformal Field Theory

2004-12-10

arxiv.org/abs/math-ph/0412033v2

Physics

Mathematical Physics

18 pages, 1 figure. v.2: section about kappa not equal to 4 deleted

Scientific paper

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.

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