Related papers: Algebraic orbifold conformal field theories
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…
Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying…
Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
For a vertex operator algebra $V$, one may naturally define spaces of conformal blocks following a construction of Frenkel-Ben-Zvi generalized by Damiolini-Gibney-Tarasca. If $V$ is strongly rational, these spaces of conformal blocks form…
Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…
A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the "nonlinear Sigma-model" or "lattice-CFT", is given. Underlying this approach to CFT is a unitary modular functor, the…
This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…
The moduli space of all rational conformal quantum field theories with effective central charge c_eff = 1 is considered. Whereas the space of unitary theories essentially forms a manifold, the non unitary ones form a fractal which lies…
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…