TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.102
TI  - $G_2$-manifolds from 4d N=1 theories, part I: Domain walls
PY  - 2024/10/03
UR  - https://scipost.org/SciPostPhys.17.4.102
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 102
A1  - Braun, Andreas P.
AU  - Sabag, Evyatar
AU  - Sacchi, Matteo
AU  - Schäfer-Nameki, Sakura
AB  - We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d $\mathcal{N}=1$ duality domain walls of 5d $\mathcal{N}=1$ 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 $\mathcal{N}=1$ 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.
ER  -

@Article{10.21468/SciPostPhys.17.4.102,
	title={{$G_2$-manifolds from 4d N=1 theories, part I: Domain walls}},
	author={Andreas P. Braun and Evyatar Sabag and Matteo Sacchi and Sakura Schäfer-Nameki},
	journal={SciPost Phys.},
	volume={17},
	pages={102},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.102},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.102},
}