Related papers: Some open problems in mathematical two-dimensional…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
Representations of the superalgebra $osp(2|2)$ and current superalgebra $osp(2|2)^{(1)}_k$ in the standard basis are investigated. All finite-dimensional typical and atypical representations of $osp(2|2)$ are constructed by the vector…
We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations. Taking the two-dimensional complex-parametrized conformal…
We calculate the interaction vertex of three BFKL states including the bare triple BFKL Pomeron coupling and discuss its relation with the correlation functions in two-dimensional conformal field theory. We construct the operator algebra of…
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
Using Wigner transforms of Green functions, we discuss non-equilibrium generalizations of spectral functions and occupation numbers. We develop methods for computing time-dependent spectral functions in conformal field theories…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
In this paper we describe all, up to isomorphism, left unital, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and $\mathbb{R}$. We tabulate the algebras with the units.
A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field…
The two pillars of rational conformal field theory and rational vertex operator algebras are modularity of characters on the one hand and its interpretation of modules as objects in a modular tensor category on the other one. Overarching…
The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…
We review some ideas from a recent construction which introduced the notion of vertex operators and form factors as vacuum expectation values of related vertex operators in the space of fields. The vertex operators are constructed…
In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of Lewellen on sewing constraints for conformal theories in the presence…
In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and…
We present part of our investigations on two dimensional N=1 and N=2 superconformal field theories. As a direct generalization we consider the SU(2) coset models, in particular their renormalization group properties. A search and possible…
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus…
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models.…