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Related papers: General Bootstrap Equations in 4D CFTs

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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

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 study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling…

High Energy Physics - Theory · Physics 2015-06-19 Luis F. Alday , Agnese Bissi

In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a…

Quantum Algebra · Mathematics 2020-06-30 Yuto Moriwaki

In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…

High Energy Physics - Theory · Physics 2026-05-05 Nathan Benjamin , A. Liam Fitzpatrick , Wei Li , Jesse Thaler

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

In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…

High Energy Physics - Theory · Physics 2019-02-06 Santiago Migliaccio

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a…

High Energy Physics - Theory · Physics 2025-12-10 Sebastian Harris

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…

High Energy Physics - Theory · Physics 2014-07-31 Miguel S. Costa , Joao Penedones , David Poland , Slava Rychkov

We propose a bootstrap program for CFTs near intersecting boundaries which form a co-dimension 2 edge. We describe the kinematical setup and show that bulk 1-pt functions and bulk-edge 2-pt functions depend on a non-trivial cross-ratio and…

High Energy Physics - Theory · Physics 2021-10-27 António Antunes

We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations. Taking the two-dimensional complex-parametrized conformal…

High Energy Physics - Theory · Physics 2018-04-03 Sergio Giardino

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…

High Energy Physics - Theory · Physics 2015-01-26 Miguel S. Costa , Joao Penedones , David Poland , Slava Rychkov

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 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

We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat…

High Energy Physics - Theory · Physics 2023-04-05 Enrico Parisini , Kostas Skenderis , Benjamin Withers

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 derive a compact analytic formula for a complete basis of conformally invariant tensor structures for three-point functions of conserved operators in arbitrary 4D Lorentz representations. The construction follows directly from a novel…

High Energy Physics - Theory · Physics 2026-01-09 Paul Heslop , Hector Puerta Ramisa

It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special property: if a scalar operator with conformal dimension $\Delta$ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary…

High Energy Physics - Theory · Physics 2015-08-12 Gideon Vos

In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…

High Energy Physics - Theory · Physics 2007-05-23 Ivan K. Kostov

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local…

High Energy Physics - Theory · Physics 2018-11-14 Luca Iliesiu , Murat Koloğlu , Raghu Mahajan , Eric Perlmutter , David Simmons-Duffin