相关论文: On Stochastic Evolutions and Superconformal Field …
Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss…
In this note, we show how to relate the Schramm-Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The conformal restriction properties of SLE that have been recently studied in the paper…
This manuscript explores the connections between a class of stochastic processes called "Stochastic Loewner Evolution" (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in…
It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable…
We describe the general features of the Neveu-Schwarz and Ramond sectors of logarithmic conformal field theories with N=1 supersymmetry. Three particular systems are examined in some detail -- D-brane recoil, a superconformal extension of…
We review the recently developed relation between the traditional algebraic approach to conformal field theories and the more recent probabilistic approach based on stochastic Loewner evolutions. It is based on implementing random conformal…
Stochastic Loewner evolutions (SLE) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLE evolutions and conformal field theories (CFT) which is…
We propose variants of Schramm-Loewner evolution (SLE) that are related to superconformal algebras following the group theoretical formulation of SLE, in which the relevant stochastic differential equation is derived from a random process…
The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions…
Formal Loewner evolution is connected to conformal field theory. In this letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of…
It is discussed how stochastic evolutions may be connected to SU(2) Wess-Zumino-Witten models. Transformations of primary fields are generated by the Virasoro group and an affine extension of the Lie group SU(2). The transformations may be…
This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the…
The construction of Neveu-Schwarz superconformal field theories for any N is given via a superfield formalism. We also review some results and definitions of superconformal manifolds and we generalise contour integration and Taylor…
One of the important aspects in recent trends in complex analysis has been the increasing degree of cross-fertilization between the latter and mathematical physics with great benefits to both subjects. Contour dynamics in the complex plane…
Superconformal change of variables formulas for N=1 Neveu-Schwarz vertex operator superalgebras are presented for general invertible superconformal changes of variables. Using the underlying worldsheet supergeometry of propagating…
It is now well known that non-local observables in critical statistical lattice models, polymers and percolation for example, may be modelled in the continuum scaling limit by logarithmic conformal field theories. Fusion rules for such…
The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial…
This monograph is dedicated to a generalization of the L\"owner equation in its stochastic form known as SLE and to its coupling with the Gaussian free field, ultimately aiming at the construction of a boundary conformal field theory with…
We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in…
As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular…