Related papers: Two Dimensional Conformal Field Theory on Open and…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
Talk presented at the conference on representation theory and harmonic analysis at Saclay, the talk presented the development in conformal field theory since 1968
We examine some of the standard features of primary fields in the framework of a $q$-deformed conformal field theory. By introducing a $q$-OPE between the energy momentum tensor and a primary field, we derive the $q$-analog of the conformal…
We describe conformal field theories, correlation functions of which satisfy equations of the two-dimensional fluid mechanics. Prediction for the energy spectrum is given, $E(k) \sim k^{-25/7}$.
We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL(2) x A for some Lie group A.…
By use of the AdS/CFT correspondence on orbifolds, models are derived which can contain the standard model of particle phenomenology. It will be assumed that the theory becomes conformally invariant at a renormalization-group fixed-point in…
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…
The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
We compute the gauge field functional integral giving the scalar product of the SU(2) Chern-Simons theory states on a Riemann surface of genus > 1. The result allows to express the higher genera partition functions of the SU(2) WZNW…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
This article develops new techniques for understanding the relationship between the three different mathematical formulations of two-dimensional chiral conformal field theory: conformal nets (axiomatizing local observables), vertex operator…
We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the…
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with…