Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2017)193
Keywords
Conformal Field Theory; Field Theories in Lower Dimensions
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Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- Simons Foundation [488659]
- STFC [ST/P000371/1] Funding Source: UKRI
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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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