Crossing symmetry in alpha space Article Swipe

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Matthijs Hogervorst , Balt C. van Rees ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1007/jhep11(2017)193 · OA: W2592707043

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.