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Related papers: Exact 3D Conformal Blocks from Fractional Calculus

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We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point…

High Energy Physics - Theory · Physics 2022-12-12 Ilija Buric , Volker Schomerus

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

We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…

High Energy Physics - Theory · Physics 2019-07-25 Jean-François Fortin , Valentina Prilepina , Witold Skiba

By Liouville's theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement of the conformal Lie algebra which is an…

Algebraic Geometry · Mathematics 2021-02-24 Mikhail Kapranov

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 present explicit recursive relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the…

High Energy Physics - Theory · Physics 2009-11-11 V. A. Belavin

We show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bundles of conformal blocks have rank one, this construction…

Mathematical Physics · Physics 2011-02-22 R. Rimányi , V. Schechtman , A. Varchenko

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

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…

High Energy Physics - Theory · Physics 2021-11-24 Rajeev S. Erramilli , Luca V. Iliesiu , Petr Kravchuk , Walter Landry , David Poland , David Simmons-Duffin

We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is analyzed in radial quantization: individual…

High Energy Physics - Theory · Physics 2013-05-22 Matthijs Hogervorst , Slava Rychkov

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

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…

High Energy Physics - Theory · Physics 2017-11-07 Volker Schomerus , Evgeny Sobko , Mikhail Isachenkov

As anticipated in [1], elaborated in [2-4], and explicitly formulated in [5], the Dotsenko-Fateev integral discriminant coincides with conformal blocks, thus providing an elegant approach to the AGT conjecture, without any reference to an…

High Energy Physics - Theory · Physics 2010-11-05 A. Mironov , A. Morozov , Sh. Shakirov

We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism…

High Energy Physics - Theory · Physics 2021-11-24 Jean-François Fortin , Wen-Jie Ma , Valentina Prilepina , Witold Skiba

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…

High Energy Physics - Theory · Physics 2019-05-02 Jean-François Fortin , Witold Skiba

These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…

Algebraic Geometry · Mathematics 2026-04-02 Chiara Damiolini

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…

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

We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and (epsilon1-deformed)…

High Energy Physics - Theory · Physics 2015-06-19 Amir-Kian Kashani-Poor , Jan Troost

We give a recursive method to compute the classical conformal blocks in Liouville field theory. The values of the expansion coefficients are given by an algebraic scheme which works to all orders. The algebraic expression of the intervening…

High Energy Physics - Theory · Physics 2025-12-23 Pietro Menotti

We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the…

High Energy Physics - Theory · Physics 2009-11-10 S. Balaska , K. Demmouche