标题： 具有离散规范对称性的6d F理论真空的扭曲几何 显示英文标题

标题： The twisted geometry of 6d F-theory vacua with discrete gauge symmetries

摘要： 我们研究了在扭曲圆环紧致化下，引力理论中的离散规范群和离散电荷的命运。 然后我们将这些结果应用于具有离散规范对称性的六维F理论真空，并将它们与支撑对偶M理论紧致化的亏格一纤维化卡拉比-丘三流形的几何结构联系起来。 这使我们引入了一类几何结构，我们称之为几乎一般的椭圆/亏格一纤维化卡拉比-丘三流形，并对其性质提出了详细的猜想。 第二次扭曲圆环紧致化将这些M理论真空与内部几何中具有平坦但拓扑非平凡B场的IIA紧致化联系起来。 在这种配置下的A模型拓扑弦分拆函数与相关F理论真空的六维非临界弦的扭曲-共轭椭圆指标密切相关。 扭曲-共轭椭圆指标的模性质暗示了新的扭曲导出等价性。 因此，我们恢复并显著扩展了物理和数学文献中的早期结果。 我们研究的一个重要结果是，如果离散规范对称性不是循环的，那么不存在光滑的亏格一纤维化来表示相关的轴子-膨胀子轮廓。 显示英文摘要

摘要： We study the fate of discrete gauge groups and discrete charges of gravitational theories under twisted circle compactification. We then apply our results to six-dimensional F-theory vacua with discrete gauge symmetries and relate them to the geometry of the genus one fibered Calabi-Yau threefolds that underlie the dual M-theory compactifications. This leads us to introduce a class of geometries, which we call almost generic elliptic/genus one fibered Calabi-Yau threefolds, and to make detailed conjectures about their properties. A second twisted circle compactification relates these M-theory vacua to Type IIA compactifications with flat but topologically non-trivial B-fields along the internal geometry. The A-model topological string partition function on such configurations is intimately tied to the twisted-twined elliptic genera of the six-dimensional non-critical strings of the associated F-theory vacuum. The modular properties of the twisted-twined elliptic genera imply new twisted derived equivalences. We thus recover and significantly extend earlier results from both the physical and the mathematical literature. An important outcome of our study is that if the discrete gauge symmetry is not cyclic, then no smooth genus one fibration exists that represents the associated axio-dilaton profile.