相关论文: SLE-type growth processes and the Yang-Lee singula…
We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman-Weinberg one-loop potential, which is…
In this paper we present explicit results for the fusion of irreducible and higher rank representations in two logarithmically conformal models, the augmented c_{2,3} = 0 model as well as the augmented Yang-Lee model at c_{2,5} = -22/5. We…
We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos…
In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a…
In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of such SDEs are obtained. Furthermore, the…
The two-dimensional Brownian loop-soup is a Poissonian random collection of loops in a planar domain with an intensity parameter c. When c is not greater than 1, we show that the outer boundaries of the loop clusters are disjoint simple…
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarithmic spirals, for example, are associated with conformal…
We address the scaling behaviour of contour-shape-dependent ultra-violet singularities of the light-like cusped Wilson loops in Yang-Mills and ${\cal N} = 4$ super-Yang-Mills theories in the higher orders of the perturbative expansion. We…
In this paper we derive the scaling fields in $c=-2$ conformal field theory associated with weakly allowed clusters in abelian sandpile model and show a direct relation between the two models.
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It…
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…
In this first of four articles, we study a homogeneous system of $2N+3$ linear partial differential equations (PDEs) in $2N$ variables that arises in conformal field theory (CFT) and multiple Schramm-Lowner evolution (SLE). In CFT, these…
Urban transportation systems grow over time as city populations grow and move and their transportation needs evolve. Typical network growth models, such as preferential attachment, grow the network node by node whereas rail and metro…
We review conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry.…
We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We consider the dimer model on the square and hexagonal lattices with doubly periodic weights. The purpose of this paper is threefold: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov (and…
We study a stochastic Laplacian growth model, where a set $\mathbf{U}\subseteq\mathbb{R}^{\mathrm{d}}$ grows according to a reflecting Brownian motion in $\mathbf{U}$ stopped at level sets of its boundary local time. We derive a scaling…
Maximally supersymmetric Yang--Mills theory (N=4 SYM) is conformal for any value of the coupling. Lattice regularization breaks conformality through the introduction of a non-zero lattice spacing and a finite lattice volume. This…