Related papers: Classification of RCFT from Holomorphic Modular Bo…
Minimal d=2 CFTs are usually classified through modular invariant partition functions. There is a finer classification of ``non complete'' models when S-duality is not imposed. We approach this classification by starting with the local…
It has been proposed that Randall-Sundrum models can be holographically described by a regularized (broken) conformal field theory. We analyze the foundations of this duality using a regularized version of the AdS/CFT correspondence. We…
We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which…
We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear…
The local logarithmic conformal field theory corresponding to the triplet algebra at c=-2 is constructed. The constraints of locality and crossing symmetry are explored in detail, and a consistent set of amplitudes is found. The spectrum of…
Although logarithmic conformal field theories (LCFTs) are known not to factorise many previous findings have only been formulated on their chiral halves. Making only mild and rather general assumptions on the structure of an chiral LCFT we…
Two dimensional conformal field theories with central charge one are discussed. After a short review of theories based on one free boson, a different CFT is described, which is obtained as a limit of minimal models.
In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was designed to capture the mathematical essence of the Conformal Bootstrap formalism pioneered in physics by Belavin-Polyakov-Zamolodchikov. In Segal's…
We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to…
The partition function of rational conformal field theories (CFTs) on Riemann surfaces is expected to satisfy ODEs of Gauss-Manin type. We investigate the case of hyperelliptic surfaces and derive the ODE system for the $(2,5)$ minimal…
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…
Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible measurable invariant line fields of a rational function on its…
We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and…
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…
The bootstrap program for 1+1-dimensional integrable Quantum Field Theories (QFT's) is developed to a large extent for the Homogeneous sine-Gordon (HSG) models. This program can be divided into various steps, which include the computation…
In a first part, we generalize a theorem for an holomorphic $\times $ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear…
In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a…
We introduce a general framework to construct many-body lattice wavefunctions starting from the conformal blocks (CBs) of rational conformal field theories (RCFTs). We discuss the different ways of encoding the physical degrees of freedom…