Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions

Abstract

We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each class have the same OPE convergence properties in s-, t- and u-channels. We give tables including the information of OPE convergence for all classes. Our work justifies that in a subset of the configuration space, Lorentzian CFT four-point functions are genuine analytic functions. Our results are valid for unitary CFTs in $d\ge 2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

v1:50+23 pages, 14 figures, 16 tables v2:a few typos corrected, figure 5,7,9,10 improved, bibliography improved v3: a quick summary added at the beginning, bibliography updated, Mathematica code added in the ancillary folder v4 template replaced v5: minor revision, a few more examples/footnotes added v6 Mathematica code added in the ancillary folder

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Cited by in corpus (2)

• Holography of Information in AdS/CFT
• The Dual Conformal Box Integral in Minkowski Space