Related papers: Universal Spinning Casimir Equations and Their Sol…
Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of…
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…
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…
Applying the Casimir operator to four-point functions in CFTs allows us to find the conformal blocks for any external operators. In this work, we initiate the program to find the superconformal blocks, using the super Casimir operator, for…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in http://arxiv.org/abs/1602.01858 in several directions. First, we explicitly demonstrate that the action of quartic…
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 compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l,\bar l) of the Lorentz group in four dimensional…
Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…
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…
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 develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions…
We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect.…
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an…
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…
We study the structure of series expansions of general spinning conformal blocks. We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…