Related papers: PCT Theorem, Wightman Axioms and Conformal Bootstr…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…
There are still no interacting models of the Wightman axioms, suggesting that the axioms are too tightly drawn. Here a weakening of linearity for quantum fields is proposed, with the algebra still linear but with the quantum fields no…
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in $D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve…
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
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…
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…
In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their $n$-point functions is unclear in this setting. An alternative approach uses…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…
We apply the analytic conformal bootstrap method to study weakly coupled conformal gauge theories in four dimensions. We employ twist conformal blocks to find the most general form of the one-loop four-point correlation function of…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…
We introduce the framework of Quantum Field Theories in general backgrounds through the lens of the path integral, in the formulation known as the Functorial QFT. With the aim of studying properties of strongly coupled QFTs, we present key…
We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and…
We review and develop a mathematical framework for nonlocal quantum field theory (QFT) with a fundamental length. As an instructive example, we reexamine the normal ordered Gaussian function of a free field and find the primitive…
We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent…
Higher-point correlation functions encode the data of infinitely many 4-point correlators in conformal field theory (CFT). In this paper, we develop new tools to efficiently extract this data from multi-point crossing equations. Concretely,…
We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the…
Groundstates of 1+1d conformal field theories (CFTs) satisfy a local entropic condition called the vector fixed point equation. This condition is surprisingly well satisfied by groundstates of quantum critical lattice models even at small…