The five-point bootstrap

A bstract We study five-point correlation functions of scalar operators in d -dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an...

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Bibliographic Details
Published in:The journal of high energy physics 2023-10, Vol.2023 (10), p.153-23, Article 153
Main Authors: Poland, David, Prilepina, Valentina, Tadić, Petar
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Conformal and W Symmetry
Correlation
Correlation Functions
Differential equations
Elementary Particles
High energy physics
Ising model
Operators (mathematics)
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scale and Conformal Symmetries
String Theory
Symmetry
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Summary:A bstract We study five-point correlation functions of scalar operators in d -dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈 σσϵσσ 〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆ cutoff . We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2023)153