SLE(kappa,rho) and Conformal Field Theory
arXiv:math-ph/0412033
Abstract
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
References in corpus (1)
Cited by in corpus (12)
- 2D growth processes: SLE and Loewner chains
- Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
- Conformal Random Geometry
- The Gaussian free field and SLE(4) on doubly connected domains
- On conformal field theory of SLE(kappa; rho)
- The scaling limit of two cluster boundaries in critical lattice models
- Critical interfaces of the Ashkin-Teller model at the parafermionic point
- On SLE martingales in boundary WZW models
- The Correlator Toolbox, Metrics and Moduli
- Conformal field theory on the Riemann sphere and its boundary version for SLE
- Hadamard's formula and couplings of SLEs with free field
- Connecting SLE and minisuperspace Liouville gravity