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arXiv · 1702.08471

Crossing Symmetry in Alpha Space

Matthijs Hogervorst·Balt C. van Rees
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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 alpha. 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.

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Matthijs Hogervorst, Balt C. van Rees. 2017-09-26. Crossing Symmetry in Alpha Space. https://doi.org/10.1007/jhep11(2017)193

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