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Asymptotic Structure of Higher Dimensional Yang-Mills Theory
by Temple He, Prahar Mitra
Submission summary
| Authors (as registered SciPost users): | Prahar Mitra |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2306.04571v2 (pdf) |
| Date submitted: | 2023-12-07 19:10 |
| Submitted by: | Mitra, Prahar |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in $(d+2)$-dimensional Minkowski spacetime for any $d \geq 2$, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in $(d+2)$-dimensional spacetime.
Author comments upon resubmission
List of changes
1. We have rewritten equation (2.19) in terms of ${\hat A}$ instead of ${\bar A}$. The new ${\hat A}$ is defined in equation (2.20).
2. We have modified the definition of $E^\pm$. The new definition is given in equation (2.20).
3. In the paragraph below equation (2.23), we previously erroneously claimed that the Coulombic part of the gauge field dies off at large $|u|$. We have fixed this in the new version by adding a new segment to the paper (Paragraph starting at equation (2.24) and ending at equation (2.28), along with footnote 8). However, the final conclusion, equation (2.28), remains unchanged.
4. In equation (2.31), we perform a mode expansion for the newly defined field ${\hat A}$, instead of ${\bar A}$. The new mode coefficients ${\bar {\cal O}}$ are defined in equation (2.32). We have replaced ${\cal O}$ with ${\bar {\cal O}}$ in equations (2.40), (3.1), (3.3), (3.4) and (3.14).
5. Minor notational change in footnote 10.
6. Fixed the formula for the large gauge charge in equation (3.15). The second term in (3.15) was previously missed.
7. Added the quantum commutators in equations (3.17) and (3.18).
Current status:
Reports on this Submission
Strengths
1) Contains new technical results relevant to an active subject
2) Unifies and simplifies previous works
3) Very clearly written
Weaknesses
1) Primarily a technical extension of previous work by the same authors
Report
This paper treats the quantization of higher-dimensional Yang-Mills theory. That is a well-tread subject, but the main goal of the work is to understand the vacuum sector of the model which has received little attention. Developments over the past several years link that sector of the model to soft theorems and asymptotic symmetries, and it seems that studying the correspondence in higher dimensions does clarify and support some of the results in $D=4$.
The analysis builds on several previous papers by the same authors and the main result is a unified treatment of even and odd dimensional cases using some properties of the shadow transform.
I would view the work primarily as a technical extension of the authors' previous analyses. The results will be of interest to different groups, but especially to those working on celestial holography and related topics. The derivation of the generalized soft theorem in non-trivial vacua is especially nice and needed to be done.
I found the paper to be very well written and clear and I would recommend publication without the need for revision.
Requested changes
None