SciPost Submission Page
Split representation in celestial holography
by Chi-Ming Chang, Reiko Liu, Wen-Jie Ma
Submission summary
| Authors (as registered SciPost users): | Chi-Ming Chang · Wenjie Ma |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00032v1 (pdf) |
| Date submitted: | 2023-12-17 09:41 |
| Submitted by: | Ma, Wenjie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We develop a split representation for celestial amplitudes in celestial holography, by cutting internal lines of Feynman diagrams in Minkowski space. More explicitly, the bulk-to-bulk propagators associated with the internal lines are expressed as a product of two boundary-to-bulk propagators with a coinciding boundary point integrated over the celestial sphere. Applying this split representation, we compute the conformal partial wave and conformal block expansions of celestial four-point functions of massless scalars and photons on the Euclidean celestial sphere. In the $t$-channel massless scalar amplitude, we observe novel intermediate exchanges of staggered modules in the conformal block expansion.
Current status:
Reports on this Submission
Strengths
1. The split representation of the AdS and dS propagators to obtain a new representation of celestial amplitudes in terms of lower point amplitudes (analogous to the conformal block expansion in a CFT)
2. The result may help us learn more about the locality and unitarity properties of CCFTs and is, therefore, interesting.
3. The presentation of the paper is clear and several examples are explored (with lengthy calculations).
Weaknesses
The split representation seems to apply to individual Feynman diagrams, not to the bulk amplitude as a whole. It is not clear what this new representation would teach us about the complete amplitude. For example, the tree-level four gluon amplitude in Yang-Mills contains 4 Feynman diagrams, contributing over 1000 terms (the five gluon amplitude has around 10000 terms), but the total amplitude is incredibly simple.
How can the split representation of the Feynman propagator be useful in this case?
Report
The paper is well-written and accompanied by a rather detailed Appendix that will be useful in future developments in celestial holography. It can potentially give new insight into the structure of celestial amplitudes.
I recommend that it be published.
Requested changes
1. Factors of $i\epsilon$ should be included in equations (4.2), (4.3), (4.4), (5.1) etc. to ensure that the relevant integrals are well-defined.
2. There is an extra "[spin?]" in the first paragraph of section 5.2. Is that a typo?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
interesting result, clean presentation, detailed appendices
Weaknesses
n/a
Report
The authors are developing a more systematic way to compute conformal partial waves for celestial amplitudes. I think this is an interesting result and I'm happy to endorse its publication. I also appreciate the efficiency in presenting the result of the paper paired with the extended pedagogy in the appendices.
Requested changes
The statements about helicity vs spin at the beginning of section 5.2 are a little confusing. I'd recommend using helicity for the 4D quantities and spin for the 2D ones if everything is massless. I don't like the sentence that the shadow flips the helicity -- I think you just mean 2D spin, hence my comment above.