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Bulk locality from the celestial amplitude
by ChiMing Chang, Yutin Huang, ZiXun Huang, Wei Li
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Submission summary
Authors (as registered SciPost users):  ChiMing Chang 
Submission information  

Preprint Link:  scipost_202109_00019v1 (pdf) 
Date submitted:  20210915 15:45 
Submitted by:  Chang, ChiMing 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
In this paper, we study the implications of bulk locality on the celestial amplitude. In the context of the fourpoint amplitude, the fact that the bulk Smatrix factorizes locally in poles of Mandelstam variables is reflected in the imaginary part of the celestial amplitude. In particular, on the positive real axes in the complex plane of the boost weight, the imaginary part of the celestial amplitude can be given as a positive expansion on the Poincar\'e partial waves, which are nothing but the projection of flatspace spinning polynomials onto the celestial sphere. Furthermore, we derive the celestial dispersion relation, which relates the imaginary part to the residue of the celestial amplitude for negative even integer boost weight. The latter is precisely the projection of low energy EFT coefficients onto the celestial sphere. We demonstrate these properties explicitly on the open and closed string celestial amplitudes. Finally, we give an explicit expansion of the Poincar\'e partial waves in terms of 2D conformal partial waves.
Current status:
Reports on this Submission
Anonymous Report 1 on 20211118 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202109_00019v1, delivered 20211118, doi: 10.21468/SciPost.Report.3870
Strengths
1. The authors carefully study the analytic properties of the celestial amplitudes. The implication of bulk locality is also emphasized.
2. In celestial CFT, one of the most puzzling aspects is crossing symmetry. The authors perform a thorough analysis of the relations between celestial correlators computed from different crossing chanels.
3. The authors demonstrated the general statements in many examples, including scalar field theory and string theory.
Weaknesses
1. While the authors uncover and demonstrate several interesting properties of the celestial amplitudes, the physical interpretation for some of the properties is not clear.
Report
This paper addresses many fundamental questions of the celestial amplitudes, including locality, analyticity, and crossing. While a comprehensive answer is still lacking, it is an important initial step towards understanding the celestial amplitudes. I therefore recommend this paper for publication with minor changes.
Requested changes
1. Above (2.6), there seems to be a missing reference.
2. It seems to me that when the authors discussed the imaginary part of the celestial amplitude, they assumed $\beta$ to be real. It is not entirely clear to me where and why did the authors make this assumption. Perhaps it's around (2.31), but the convergence of the Mellin integral seems to allow for an imaginary part of $\beta$.
3. There seems to be a typo in the $z(1z)$ factor in the first line of (5.1).
4. The analytic property (5.5) is very interesting. Can the authors provide some physical interpretation? Should we view (5.5) as the crossing symmetry for the celestial amplitudes?
Author: ChiMing Chang on 20220128 [id 2125]
(in reply to Report 1 on 20211118)We thank the referee for the comments, and will resubmit to address referee's points.