Related papers: Calculus of conformal fields on a compact Riemann …

We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincar\'e dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow…

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and…

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…

Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…

This is a brief introduction to the subject of Conformal Field Theory on surfaces with boundaries and crosscaps, which describes the perturbative expansion of open string theory.

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis…

In this paper we consider the interrelation between compactified string theories on torus and gauge fields on it. We start from open string theories with background gauge fields and derive partition functions by path integral. Since the…

It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal…

It is known that the Takahashi--Tanimoto identity-based solution in open string field theory derives a kinetic operator which is a sum of twisted Virasoro generators. Applying the infinite circumstance description of conformal field theory,…

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.…

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…

This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention.…

We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…

Knizhnik-Zamolodchikov-Bernard equations for twisted conformal blocks on compact Riemann surfaces with marked points are written explicitly in a general projective structure in terms of correlation functions in the theory of twisted b-c…

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based…

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…

We consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We approach this using the theory of modular operads by introducing a new…

The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…

Aspects of parity-preserving, three-dimensional conformal field theories (CFTs) with a global $U(1)$ symmetry in the presence of a background magnetic field are investigated. A local effective action is constructed to four-derivative order,…