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Families of solutions of the heterotic G$_2$ system
by Xenia de la Ossa, Mateo Galdeano
Submission summary
| Authors (as registered SciPost users): | Mateo Galdeano · Xenia de la Ossa |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202206_00009v2 (pdf) |
| Date submitted: | 2023-02-15 20:54 |
| Submitted by: | Galdeano, Mateo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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.
Author comments upon resubmission
We submit a revised version of our manuscript, where the revisions suggested by the referees have been addressed.
List of changes
•We have replaced the terminology “coset space” by “homogeneous space” throughout the whole text.
• p. 5 We have replaced the verb “form” by “generate”.
• p. 6 We have rewritten the second paragraph and added a brief footnote pointing out why the construction of such a basis is possible.
• p. 7 We have rewritten the expression of ∗F2 in eq. (2.11) to avoid confusion.
• p. 8 We have rewritten and reordered the paragraphs at the beginning of section 2.2. As the referee pointed out, our statement about the Maurer–Cartan form defining a metric was incorrect so we have included a new discussion regarding the metric in a footnote that appears on page 9.
• p. 8 We have amended the wrong statement of m being a Lie subalgebra.
• p. 14 We have corrected the statement about the SU(2)-bundle being identified with the bundle of self-dual forms.
• p. 18 We have corrected an incorrect statement about the adjoint representation.
• p. 25 We have clarified that we are speaking about the range of values of s.
• p. 26 We have added a paragraph in the introduction of section 5 commenting on how we denote the solutions throughout the whole section.
• p. 36 We have added a paragraph commenting on the possibility of having a disconnected moduli space.
•We have also amended some harmless typos present in the text and that we have detected since the submission of the manuscript.