Crossing symmetry in alpha space

Hogervorst, Matthijs; van Rees, Balt C.

Abstract

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.

Citation

Hogervorst, M., & van Rees, B. C. (2017). Crossing symmetry in alpha space. Journal of High Energy Physics, 2017(11), Article 193. https://doi.org/10.1007/jhep11%282017%29193

• 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
• DOI: https://doi.org/10.1007/jhep11%282017%29193