Related papers: On SLE martingales in boundary WZW models

Correlation functions and form factors in vertex models or spin chains are known to satisfy certain difference equations called the quantum Knizhnik-Zamolodchikov equations. We find similar difference equations for the case of semi-infinite…

We present a relation between conformal field theories (CFT) and radial stochastic Schramm-Loewner evolutions (SLE) similar to that we previously developed for the chordal SLEs. We construct an important local martingale using degenerate…

This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…

In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution and the KPZ relation in a natural way, shedding new light on all of them. Our principal result shows that the level lines and the SLE$_\kappa$ flow lines of the…

We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\kappa$ loop measures for $\kappa\in(0,8)$. First, we construct rooted SLE$_\kappa$ loop measures in the Riemann sphere $\widehat{\mathbb…

We analyze boundary states in the SU(2)$_k$ WZW model using open string field theory in the level truncation approximation. We develop algorithms that allow effective calculation of action in this model and we search for classical solutions…

The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier-Miller-Sheffield (2014). In this paper we consider the mating of trees…

We derive the Ward identities of Conformal Field Theory (CFT) within the framework of Schramm-Loewner Evolution (SLE) and some related processes. This result, inspired by the observation that particular events of SLE have the correct…

It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give conformal welding of quantum surfaces. Motivated by a generalization of conformal…

The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter kappa equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has…

Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma…

We study the Loewner evolution whose driving function is $W_t = B_t^1 + i B_t^2$, where $(B^1,B^2)$ is a pair of Brownian motions with a given covariance matrix. This model can be thought of as a generalization of Schramm-Loewner evolution…

For the case of the SU(2) WZW model at level one, the boundary states that only preserve the conformal symmetry are analysed. Under the assumption that the usual Cardy boundary states as well as their marginal deformations are consistent,…

We derive a surprising correspondence between SLE$_{\kappa}(\rho)$ processes and light cones of the Gaussian free field (GFF). Recall that (one-sided, chordal, origin-seeded) SLE$_\kappa(\rho)$ processes are in some sense the simplest and…

We give a simplified and complete proof of the convergence of the chordal exploration process in critical FK-Ising percolation to chordal SLE$_\kappa( \kappa-6)$ with $\kappa=16/3$. Our proof follows the classical excursion-construction of…

The scaling limit of planar loop-erased random walks is described by a stochastic Loewner evolution with parameter kappa=2. In this note SLE(2) in the upper half-plane H minus a simply-connected compact subset K of H is studied. As a main…

An annulus SLE$_\kappa$ trace tends to a single point on the target circle, and the density function of the end point satisfies some differential equation. Some martingales or local martingales are found for annulus SLE$_4$, SLE$_8$ and…

This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and…

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of…

We prove that for $\kappa\in(0,8)$, if $(\eta_1,\eta_2)$ is a $2$-SLE$_\kappa$ pair in a simply connected domain $D$ with an analytic boundary point $z_0$, then $\lim_{r\to 0^+}r^{-\alpha} \mathbb{P}[\mbox{dist}(z_0,\eta_j)<r,j=1,2]$…