Related papers: Exact 3D Conformal Blocks from Fractional Calculus
We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as…
We show how to refine conformal block expansion convergence estimates from hep-th/1208.6449. In doing so we find a novel explicit formula for the 3d conformal blocks on the real axis.
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks' in three…
The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1…
A convolution approach leading to an explicit computation of a value of a 4F3 function is outlined. We also investigate about the role of the dilogarithm reflection formula, leading to a remarkable consequence: in some cases, values of 4F3…
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…
We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
We observe that conformal blocks of scalar 4-point functions in a $d$-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled…
Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra's radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension…
Conformal blocks for four point functions for fields with arbitrary spins in two dimensions are obtained by evaluating an appropriate integral. The results are just products of hypergeometric functions of the conformally invariant cross…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary quasi-primary operators. The $H$-function was introduced in a previous article and it has several…
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…
Conformal blocks are the building blocks for correlation functions in conformal field theories. The four-point function is the most well-studied case. We consider conformal blocks for $n$-point correlation functions. For conformal field…
Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable Calogero-Sutherland Hamiltonian in order to develop a…
Monoidal product, braiding, balancing and weak duality are pieces of algebraic information that are well-known to have their origin in oriented genus zero surfaces and their mapping classes. More precisely, each of them correspond to…
We present a simple prescription for computing conformal blocks and correlation functions holographically in AdS$_3$ in terms of Wilson lines merging at a bulk vertex. This is shown to reproduce global conformal blocks and heavy-light…