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

by Jiaxin Qiao

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Submission summary

Authors (as registered SciPost users): Jiaxin Qiao
Submission information
Preprint Link: scipost_202208_00075v1  (pdf)
Date accepted: 2022-09-01
Date submitted: 2022-08-28 15:06
Submitted by: Qiao, Jiaxin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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 $d\geq2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

Author comments upon resubmission

I have revised the manuscript according to the suggestions by the referees and the editor.

List of changes

According to referee 1:
1. (suggestion 1) Added footnote 4 about the domain of the four-point function.
2. (suggestion 2) Added a comment on the "linear growth condition" at the end of section 6.3.2.
3. (suggestion 4) Added an example concerning different but conformally equivalent causal orderings (section 5.6.2).
4. (suggestion 5) Completed the sentences in summary section 2.2.

According to referee 2:
5. (suggestion 1) Modified the argument on the analyticity of $u^\Delta$ after eq.(34).
6. (suggestion 2) Added explanation in the proof of lemma 3.2.
7. (suggestion 3) Added footnote 9.

According to editor:
8. Added section 5.6.1 on the general time-ordered correlation functions (with the previous section 5.6.1 included). Comment about the maximally-out-of-time-order at the end of section 5.6.1.

Published as SciPost Phys. 13, 093 (2022)

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