Related papers: Conformal field theory: a case study
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…
We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…
What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields,…
We construct topological Wess-Zumino term for supercoset sigma-models on various AdS(3) backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover,…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
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.
The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between…
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
We explain the basics of conformal theory using the language of chiral algebras of Beilinson and Drinfeld.
We give explicit field theoretical representations for the observables of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. To test our identification we compute some basic Wilson loop correlators…
A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…
Gauged Wess-Zumino-Witten theory for compact groups is considered. It is shown that this theory has fermionic BRST-like symmetry and may be exactly solved using localization approach. As an example we calculate functional integral for the…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant $\b > 0$ and the theory…
We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $\theta$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic…