Related papers: Fusion rules in conformal field theory
Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply…
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
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 study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These…
We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is analyzed in radial quantization: individual…
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a…
It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the…
Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
We review recent work in machine learning aspects of conformal field theory and Lie algebra representation theory using neural networks.
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 systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of…
We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories.…
Pseudo conformal field theories are theories with the same fusion rules, but with different modular matrix as some conventional field theory. One of the authors defined these and conjectured that, for bosonic systems, they can all be…
We determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an…
The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a…
We consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U$(1)$ gauge field, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk…