Crossing Symmetry in Alpha Space

Understand

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.