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We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical Lie algebras.

Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.

We apply Kadanoff's theory of marginal deformations of conformal field theories to twistfield deformations of Z_2 orbifold models in K3 moduli space. These deformations lead away from the Z_2 orbifold sub-moduli-space and hence help to…

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…

We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…

Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.

We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…

We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.

Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…

We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.

These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…

We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…

The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…

Talk presented at the conference on representation theory and harmonic analysis at Saclay, the talk presented the development in conformal field theory since 1968

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…

Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…