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Families of solutions of the heterotic G$_2$ system
by Xenia de la Ossa, Mateo Galdeano
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Submission summary
| Authors (as registered SciPost users): | Mateo Galdeano · Xenia de la Ossa |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202206_00009v1 (pdf) |
| Date submitted: | 2022-06-09 18:09 |
| Submitted by: | Galdeano, Mateo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct new families of solutions of the heterotic G$_2$ system on squashed homogeneous 3-Sasakian manifolds, that is, using squashed metrics on either the 7-sphere or the Aloff-Wallach space $N_{1,1}\,$. We obtain AdS$_3$ solutions for all values of the squashing parameter $s$ except for the nearly-parallel G$_2$ value $s={\scriptstyle{1/\sqrt{5}}} \,$, for which we don't find any solutions. Along the process, we construct different G$_2$-instanton connections on bundles over these squashed manifolds.
Current status:
Reports on this Submission
Strengths
- Very welcome new solutions to complicated system of equations
- Inclusion of several different families of instantons
- Very nice literature survey
Weaknesses
Primarily an imprecise use of terminology, as listed in more detailed list below.
Report
I warmly recommend this paper for acceptance, after some minor changes for clarity. The results are very welcome, and give new understanding to the system in general.
Requested changes
As listed in the attached document.
Strengths
1) Excellent exposition of the state of the art concerning heterotic G2 systems
2) Explicit construction of new AdS3 solutions
Weaknesses
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Report
Heterotic G2 systems are the most general solution of heterotic strings with 3D N=1 supersymmetry. Having pioneered work on the subject, the authors construct explicit examples based on squashings of 3-Sasakian spaces. From a technical perspective, the key is to realize these as coset spaces.
The challenge in constructing such solutions arises from the necessity to specify several structures subject to compatibility conditions: a manifold with integrable G2 structure, a vector bundle with G2 instanton connection, a G2 instanton connection for the tangent bundle, and the three-form H.
Realizing the manifolds in questions as cosets, the authors manage to explictely construct several instanton connections which typically depend on the squashing parameter s. This makes it possible to check for which choices of connection for the tangent and vector bundle and which values of s solutions to the equations of motion can be found. The solutions found are all AdS3, which implies that no hidden supersymmetry enhancement can happen.
This paper is very well written, the authors clearly explain how the solutions are constructed and neatly summarize their findings. This is supplemented by a nice review of the literature on results used.
The results of this paper will certainly serve as an interesting starting point for further investigations of heterotic G2 systems. In particular, it will be interesting to use them to exemplify the results on moduli spaces of heterotic G2 systems.
From a physics point of view not all of these solutions are acceptable as alpha' cannot necessarily be made small.
Requested changes
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Author: Mateo Galdeano on 2023-02-15 [id 3360]
(in reply to Report 2 on 2023-01-18)We are very grateful for the very precise and sharp remarks provided by the referee in the report. We have just submitted a new version of the manuscript addressing the suggested revisions, with a detailed list of changes. We also attach to this reply a PDF with that list of changes.
Attachment:
Reply_to_report.pdf