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$G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
by Andreas P. Braun, Evyatar Sabag, Matteo Sacchi, Sakura Schafer-Nameki
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Submission summary
| Authors (as registered SciPost users): | Matteo Sacchi |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2304.01193v1 (pdf) |
| Date submitted: | 2024-05-01 16:17 |
| Submitted by: | Sacchi, Matteo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N=1 duality domain walls of 5d N=1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field theory. Our starting point is the geometric realization of such a 5d superconformal field theory and its extended Coulomb branch in terms of M-theory on a non-compact singular Calabi-Yau three-fold and its K\"ahler cone. We construct the 7-manifold that realizes the domain wall in M-theory by fibering the Calabi-Yau three-fold over a real line, whilst varying its K\"ahler parameters as prescribed by the domain wall construction. In particular this requires the Calabi-Yau fiber to pass through a canonical singularity at the locus of the domain wall. Due to the 4d N=1 supersymmetry that is preserved on the domain wall, we expect the resulting 7-manifold to have holonomy $G_2$. Indeed, for simple domain wall theories, this construction results in 7-manifolds, which are known to admit torsion-free $G_2$-holonomy metrics. We develop several generalizations to new 7-manifolds, which realize domain walls in 5d SQCD theories and walls between 5d theories which are UV-dual.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-7-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.01193v1, delivered 2024-07-20, doi: 10.21468/SciPost.Report.9435
Strengths
1 - The paper connects known field theoretic results in 5d with nice geometric engineering perspectives
2 - The paper has explicit and detailed computations which should be very useful for further investigations
Weaknesses
No weaknesses
Report
In this paper the authors geometrize (find an underlying manifold with $G_2$ holonomy) a class of 4d duality domain wall theories in 5d. The two theories the domain wall interpolates between, are UV dual to each other. Such domain walls were studied field theoretically by Gaiotto and Kim in the past. For general 5d QFTs there is no algorithmic way to derive the theory living on such domain walls. The field theoretic procedure roughly amounts to guessing a theory living on the wall and performing numerous consistancy checks, e. g. studying anomalies. The understanding of such domain walls using geometric engineering in this paper provides a promising pathway into a more algorithmic study of the domain walls by embedding them in the larger string theoretic construction. Beyond the intrinsic interest in such constructions the domain wall theories studied in this paper play an important role in understanding compactifications of 6d SCFTs to 4d. As such progress on understanding them will likely lead to larger impact, e.g. better understanding of 4d supersymmetric physics.
The paper is very well written and easy to follow. It contains detailed computations and interesting results which should be of interest to a broader community interested in supersymmetric quantum field theories in dimensions 4-6. I recommend it to be published in its current form.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 1) on 2024-6-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.01193v1, delivered 2024-06-17, doi: 10.21468/SciPost.Report.9257
Report
This manuscript provides a novel physical procedure for constructing non-compact G2 manifolds by analyzing domain walls in 5D N=1 QFTs, which is systematically implemented in several families of cases. The outcome not only reproduced some non-compact 7d manifolds with explicitly known G2 metrics but also produced many more non-compact 7d manifolds on which G2 metrics are physically justified to exist.
I would recommend publication of this manuscript after the authors considered the following comments/suggestions.
Requested changes
One major comment:
The main objective of this paper is to construct a large family of non-compact G2 manifolds based on physical reasonings. Therefore, the part of ``geometrical checks" is a key component of the paper, since they reproduce specific mathematical results on G2 spaces and provide physics-based conjectures. To emphasize its key role, I recommend that the authors consider repackaging this part into an independent concise appendix, where results are stated purely in the mathematical language. For example, it would be nice to collect individual G2 geometries obtained in each section into that appendix.
The purpose would be to guide a mathematician with little knowledge of string theory to navigate through your paper with minimal effort. For that, it will be helpful to use terms such as "physic-based conjectures/hypothesis", make statements in mathematical terms, and put the minimal amount of necessary physical reasoning in quotation marks.
Minor comments:
1. On P4, "Utilizing this, allows us" -> maybe "Utilizing this allows us"
2. On P8, "Note that is equivalently ..." -> maybe "Note that this is equivalently ..."
3. On P9, "in depth" -> "in-depth"
4. On P10, "UV-duality-walls" -> "UV-duality walls"
5. On P37, "Lowering the connection": here it helps to refer to Figure 8 once more.
6. On P46: "The toric polygon for for ..." -> remove the extra "for"
7. On P50: "where similarly to the case N=2 with flavors m_\lambda" -> add a comma after "flavors"
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)