Report on 2005.09105v4

Résumé

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 ≥ 2. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

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