Related papers: Four-Point Functions in Logarithmic Conformal Fiel…

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…

The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in…

A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the…

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…

In $\mathcal{N}=1$ superconformal theories in four dimensions the two-point function of superconformal multiplets is known up to an overall constant. A superconformal multiplet contains several conformal primary operators, whose two-point…

We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…

We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…

Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…

We analyse the general structure of the three-point functions involving conserved higher-spin currents $J_{s} := J_{\alpha(i) \dot{\alpha}(j)}$ belonging to any Lorentz representation in four-dimensional conformal field theory. Using the…

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all…

We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve…

We consider 3-point and 4-point correlation functions in a conformal field theory with a W-algebra symmetry. Whereas in a theory with only Virasoro symmetry the three point functions of descendants fields are uniquely determined by the…

In this paper we develop a general method for constructing 3-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on 2-point functions. The results are provided in terms of triangular…

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for…

We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…

All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the…

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…

In these notes we discuss the procedure how to calculate nullvectors in general indecomposable representations which are encountered in logarithmic conformal field theories. In particular, we do not make use of any of the restrictions which…

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is…