Related papers: Distributions in CFT I. Cross-Ratio Space
We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some…
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…
The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We derive model-independent lower bounds on the stress tensor central charge C_T in terms of the operator content of a 4-dimensional Conformal Field Theory. More precisely, C_T is bounded from below by a universal function of the dimensions…
We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as $p^2 \to 0$. In particular, we study a form factor…
We use the correspondence between scalar field theory on AdS and induced conformal field theory on its boundary to calculate correlation functions of logarithmic conformal field theory in arbitrary dimensions.Our calculations utilize the…
We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on…
We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs). This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…
We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and…
The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental…
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…
We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in…
The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The used algorithm is described and we present all results for Jordan-rank $r=2$ and $r=3$ where we make use of…
We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any…
We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational,…
We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each…