Crossing symmetry in alpha space

A bstract We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α . This leads to...

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Bibliographic Details
Published in:The journal of high energy physics 2017-11, Vol.2017 (11), p.1-43, Article 193
Main Authors: Hogervorst, Matthijs, van Rees, Balt C.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Conformal Field Theory
Correlators
Decomposition
Eigenvectors
Elementary Particles
Field Theories in Lower Dimensions
Field theory
High energy physics
Liouville equations
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Sturm-Liouville theory
Symmetry
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Summary:A bstract We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α . This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2017)193