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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 |
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| Preprint Link: | https://arxiv.org/abs/2304.01193v2 (pdf) |
| Date accepted: | 2024-09-13 |
| Date submitted: | 2024-09-03 18:02 |
| Submitted by: | Sacchi, Matteo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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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.
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List of changes
We modified the manuscript following the minor comments of the first referee. These include mainly typos, rephrasings and references.
Published as SciPost Phys. 17, 102 (2024)