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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2304.01193 |
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| _version_ | 1866912053540683776 |
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| author | Braun, Andreas P. Sabag, Evyatar Sacchi, Matteo Schafer-Nameki, Sakura |
| author_facet | Braun, Andreas P. Sabag, Evyatar Sacchi, Matteo Schafer-Nameki, Sakura |
| contents | 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 Kähler 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 Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01193 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls Braun, Andreas P. Sabag, Evyatar Sacchi, Matteo Schafer-Nameki, Sakura High Energy Physics - Theory Differential Geometry 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 Kähler 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 Kähler 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. |
| title | $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls |
| topic | High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2304.01193 |