Related papers: Counting Conformal Correlators
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…
We study the general structure of correlation functions in an Sp(2n)-invariant formulation of systems of an infinite number of higher-spin fields. For n=4,8 and 16 these systems comprise the conformal higher-spin fields in space-time…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…
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…
We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current…
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
We consider conformal perturbation theory for $n$-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size $\epsilon$ around the…
In this work, we exploit the operator content of the $(D_{4}, A_{6})$ conformal algebra. By constructing a $Z_{2}$-invariants fusion rules of a chosen subalgebra and by resolving the bootstrap equations consistent with these rules, we…
We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
We present a comprehensive method for the evaluation of a vast class of integrals representing 3-point functions of conformal field theories in momentum space. The method leads to analytic, closed-form expressions for all scalar and…
There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in…
In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with…
In this note we present a simple method of constructing general conformally invariant three point functions of operators of various spins in three dimensions. Upon further imposing current conservation conditions, we find new parity…
We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and…
We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial…
We construct superconformal invariants in superspace which are used to build 3-point correlators of spinning operators in general $\cal{N}=2$ superconformal field theories in three dimensions. Our systematic analysis includes various…
We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1 \leq \mathcal{N} \leq 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors…
We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic…