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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…

High Energy Physics - Theory · Physics 2025-08-18 Denis Karateev , Petr Kravchuk , David Simmons-Duffin

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…

High Energy Physics - Theory · Physics 2020-01-29 Rajeev S. Erramilli , Luca V. Iliesiu , Petr Kravchuk

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of…

High Energy Physics - Theory · Physics 2022-05-23 David Poland , Valentina Prilepina

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…

High Energy Physics - Theory · Physics 2020-10-28 Ilija Buric , Mikhail Isachenkov , Volker Schomerus

Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear combination of blocks of a d-dimensional…

High Energy Physics - Theory · Physics 2021-04-07 Sarah Hoback , Sarthak Parikh

We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as…

High Energy Physics - Theory · Physics 2022-12-15 Jean-François Fortin , Jingping Li , Alex Sandomirsky , Witold Skiba

Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary…

High Energy Physics - Theory · Physics 2015-09-30 Eric Perlmutter

We compute the most general superconformal blocks for scalar operators in $4\mathcal{D}$ $\mathcal{N}=1$ superconformal field theories. Specifically we employ the supershadow formalism to study the four-point correlator $\langle\Phi_1…

High Energy Physics - Theory · Physics 2016-02-24 Zhijin Li , Ning Su

We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1…

High Energy Physics - Theory · Physics 2014-12-05 Zuhair U. Khandker , Daliang Li , David Poland , David Simmons-Duffin

We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible…

High Energy Physics - Theory · Physics 2016-01-26 Emtinan Elkhidir , Denis Karateev , Marco Serone

Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we…

High Energy Physics - Theory · Physics 2020-06-24 Sarthak Parikh

Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials. Using this presentation we give a generating set in the space of conformal blocks at any level if the marked…

Quantum Algebra · Mathematics 2009-11-18 R. Rimanyi , A. Varchenko

The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…

High Energy Physics - Theory · Physics 2020-07-15 Jean-François Fortin , Witold Skiba

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…

High Energy Physics - Theory · Physics 2025-10-07 James Halverson , Joydeep Naskar , Jiahua Tian

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…

High Energy Physics - Theory · Physics 2016-01-26 Alejandro Castedo Echeverri , Emtinan Elkhidir , Denis Karateev , Marco Serone

We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_\beta \times \mathbb{S}^3$. This is done by evaluating a class of integrals over the…

High Energy Physics - Theory · Physics 2025-08-08 Martin Ammon , Jakob Hollweck , Tobias Hössel , Katharina Wölfl

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…

High Energy Physics - Theory · Physics 2019-03-27 Israel A. Ramírez

We present a detailed study of spectrally flowed four-point functions in the SL(2,$\mathbb{R}$) WZW model, focusing on their conformal block decomposition. Dei and Eberhardt conjectured a general formula relating these observables to their…

High Energy Physics - Theory · Physics 2024-06-07 Sergio Iguri , Nicolas Kovensky , Julian H. Toro

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…

High Energy Physics - Theory · Physics 2016-08-24 Miguel S. Costa , Tobias Hansen , João Penedones , Emilio Trevisani

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…

High Energy Physics - Theory · Physics 2015-06-26 Michael Flohr , Marco Krohn