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Crossing symmetry in alpha space

Hogervorst, Matthijs; van Rees, Balt C.

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Matthijs Hogervorst

Balt C. van Rees


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.


Hogervorst, M., & van Rees, B. C. (2017). Crossing symmetry in alpha space. Journal of High Energy Physics, 2017(11), Article 193.

Journal Article Type Article
Acceptance Date Nov 16, 2017
Online Publication Date Nov 28, 2017
Publication Date Nov 28, 2017
Deposit Date Dec 13, 2017
Publicly Available Date Dec 13, 2017
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2017
Issue 11
Article Number 193


Published Journal Article (803 Kb)

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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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