相关论文: Note on SLE and logarithmic CFT

We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in…

By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary…

We study the $c=-2$ model of logarithmic conformal field theory in the presence of a boundary using symplectic fermions. We find boundary states with consistent modular properties. A peculiar feature of this model is that the vacuum…

We demonstrate how to obtain integrable results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity (LQG). In particular, we prove an exact…

We propose a generalization of Schramm-Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie…

Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution…

We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.

In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the…

We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of…

We review recent work in machine learning aspects of conformal field theory and Lie algebra representation theory using neural networks.

We review the definition of bulk and boundary conformal field theory in a way suited for logarithmic conformal field theory. The notion of a maximal bulk theory which can be non-degenerately joined to a boundary theory is defined. The…

A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…

We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…

We introduce a framework for two-dimensional conformal field theory (CFT) in the language of analytic number theory. Attached to the torus partition function of every two-dimensional CFT is a self-dual, degree-4 $L$-function of root number…

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit,…

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

We study $(m)$-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find logarithmic divergence for these correlation functions. We justify the logarithmic…

In the present paper, degeneration phenomena in conformal field theories are studied. For this purpose, a notion of convergent sequences of CFTs is introduced. Properties of the resulting limit structure are used to associate geometric…

Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory.…

We propose a contour integral representation for the one-point correlators at genus one of the primaries of a family of rational logarithmic conformal field theories.