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Journal of High Energy Physics

, 2017:193 | Cite as

Crossing symmetry in alpha space

  • Matthijs Hogervorst
  • Balt C. van Rees
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Conformal Field Theory Field Theories in Lower Dimensions 

Notes

Open Access

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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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.C.N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookU.S.A.
  2. 2.Centre for Particle Theory & Department of Mathematical SciencesDurham UniversityDurhamU.K.

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