Related papers: Dimensional Reduction for Conformal Blocks
We study conformal symmetry breaking differential operators which map differential forms on $\mathbb{R}^n$ to differential forms on a codimension one subspace $\mathbb{R}^{n-1}$. These operators are equivariant with respect to the conformal…
The exceptional superalgebra $D(2,1;\alpha)$ has been classified as a candidate conformal supersymmetry algebra in two dimensions. We propose an alternative interpretation of it as extended BFV-BRST quantisation superalgebras in 2D…
The excitation spectrum of specific conformal field theories (CFT) with central charge $c=1$ can be described in terms of quasi-particles with charges $Q=-p,+1$ and fractional statistics properties. Using the language of Jack polynomials,…
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific $q$-hypergeometric integrals whose key building block is the…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in…
It is known that a large class of characters of 2d conformal field theories (CFTs) can be written in the form of a Nahm sum. In \cite{Zagier:2007knq}, D. Zagier identified a list of Nahm sum expressions that are modular functions under a…
Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher…
In the first part of this paper, we extend the d-dimensional unitarity cut method of hep-ph/0609191 to cases with massive propagators. We present formulas for integral reduction with which one can obtain coefficients of all pentagon, box,…
Every renormalization group flow in $d$ spacetime dimensions can be equivalently described as spectral deformations of a generalized free CFT in $(d-1)$ spacetime dimensions. This can be achieved by studying the effective action of the…
In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that…
We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space…
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…
Various aspects of spaces of chiral blocks are discussed. In particular, conjectures about the dimensions of irreducible sub-bundles are reviewed and their relation to symmetry breaking conformal boundary conditions is outlined.
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around…
We study the renormalization group flow equations for correlation functions of weakly coupled quantum field theories in AdS. Taking the limit where the external points approach the conformal boundary, we obtain a flow of conformally…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
We show that conformal blocks divisors of type B_r and D_r at level one are effective sums of boundary divisors of $\bar{M}_{0,n}$. We also prove that the conformal blocks divisor of type $B_r$ at level 1 with weights…