Related papers: Conformal Blocks in Three Dimensions
We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS$_3$/CFT$_2$ correspondence. To give such an interpretation in previous studies, certain restrictions…
Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory.…
In this note we discuss some aspects of the frame formulation of conformal higher spins in three dimensions. We give some exact formulae for the coupled spin two - spin three part of the full higher spin theory and propose a star product…
We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity…
We systematically classify all possible poles of superconformal blocks as a function of the scaling dimension of intermediate operators, for all superconformal algebras in dimensions three and higher. This is done by working out the…
Zero modes of modular Hamiltonian of one interval are found in momentum space for two dimensional massless free scalar theory. Finite correlators are extracted from separate region connected correlation functions with the insertion of zero…
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby CFTs. We show that the…
By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1…
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…
We consider large-$c$ $n$-point Virasoro blocks with $n-k$ background heavy operators and $k$ perturbative heavy operators. Conformal dimensions of heavy operators scale linearly with large $c$, while splitting into background/perturbative…
We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in $d$ dimensions. We argue that these theories can be consistently defined as free CFTs…
The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…
We develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly…
The Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous…
This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the…
We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non…
This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks 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…
The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being…