AI 中文总结
受四维N=1箭图规范理论的量子场论构造启发，通过六维SCFT紧化的几何方案，构造了新的G₂-完整7维流形，在M理论中几何实现相关箭图。
AI 中文摘要
受流形到超共形场论（SCFT）的四维N=1箭图规范理论的量子场论构造启发，我们构造了G₂-完整的7维流形，在M理论中几何地实现这些箭图。场论上，四维箭图由六维N=(1,0) SCFT的通量环面紧化得到。六维理论在圆上紧化产生五维KK理论，其几何实现为M理论在非紧椭圆纤维化卡拉比-丘三维流形上。遵循场论方案，这些局域几何在圆上纤维化以实现（拓扑）G₂-完整流形。我们在秩1 E弦理论及其四维箭图的情形下具体实现，构造了新的G₂-完整空间族。
英文摘要
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.
Comments72 pages
