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arXiv · 2608.21238

$G_2$-Manifolds from 4d $\mathcal{N}=1$ Quivers

Andreas P. Braun·Oscar Lewis·Matteo Sacchi·Sakura Schafer-Nameki
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Abstract

Inspired by quantum field-theoretic constructions of 4d $\mathcal{N}=1$ quiver gauge theories that flow to superconformal field theories (SCFTs), we construct 7d manifolds of $G_2$-holonomy, which geometrically engineer these quivers in M-theory. Field theoretically, the 4d quivers are obtained by flux torus compactifications of 6d $\mathcal{N}=(1,0)$ SCFTs. The 6d theory compactified on a circle gives rise to a 5d KK-theory, which has a geometric realization as M-theory on a non-compact elliptically fibered Calabi-Yau threefold. Following the field-theoretical prescription, these local geometries are fibered over a circle to realize (topological) $G_2$-holonomy manifolds. We carry this out concretely in the case of the rank 1 E-string theory and its 4d quivers and construct new families of $G_2$-holonomy spaces.

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Andreas P. Braun, Oscar Lewis, Matteo Sacchi, Sakura Schafer-Nameki. 2026-08-21. $G_2$-Manifolds from 4d $\mathcal{N}=1$ Quivers. https://arxiv.org/abs/2608.21238

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