Crossing Symmetry in Alpha Space
High Energy Physics - Theory
2018-01-17 v2
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.
Cite
@article{arxiv.1702.08471,
title = {Crossing Symmetry in Alpha Space},
author = {Matthijs Hogervorst and Balt C. van Rees},
journal= {arXiv preprint arXiv:1702.08471},
year = {2018}
}
Comments
34 pages, 3 figures. v2: some minor changes and added subsection 2.3 on convergence