Related papers: An algebraic approach to logarithmic conformal fie…
To study the representation category of the triplet W-algebra W(p) that is the symmetry of the (1,p) logarithmic conformal field theory model, we propose the equivalent category C(p) of finite-dimensional representations of the restricted…
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of…
We study the logarithmic superconformal field theories. Explicitly, the two-point functions of N=1 logarithmic superconformal field theories (LSCFT) when the Jordan blocks are two (or more) dimensional, and when there are one (or more)…
In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify…
Some of the consequences that follow from the C_2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C_2 condition has only finitely many n-point functions, and this result is used to…
We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each…
We review recent work in machine learning aspects of conformal field theory and Lie algebra representation theory using neural networks.
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
We classify certain non-linear Lie conformal algebras with three generators, which can be viewed as deformations of the current Lie conformal algebra of sl_2. In doing so we discover an interesting 1-parameter family of non-linear Lie…
We study two-dimensional non-abelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (Gromov-Witten invariants). We found that the…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's $c$-theorem, Wess-Zumino-Witten models, modular invariant partition…
After a short review of the algebraic setting of N=2 superconformal field theories, their chiral ring and their perturbations, I present some recent results on curious relations between the integrability of their perturbations and algebraic…
We study logarithmic operators in Coulomb gas models, and show that they occur when the ``puncture'' operator of the Liouville theory is included in the model. We also consider WZNW models for $SL(2,R)$, and for SU(2) at level 0, in which…
We provide a brief but self-contained review of two-dimensional conformal field theory, from the basic principles to some of the simplest models. From the representations of the Virasoro algebra on the one hand, and the state-field…
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 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…
We present remarkable properties of the groups SL2(Z/NZ) which might be useful in detailed studies of some quotients appearing in Conformal Field Theories.
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 review some results recently obtained for the conformal field theories based on the affine Lie superalgebra osp(1|2). In particular, we study the representation theory of the osp(1|2) current algebras and their character formulas. By…