发表机构
The City College of the CUNY; The Graduate School and University Center, The City University of New York; Universidad de Oviedo; Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（纽约市立大学学院; 纽约市立大学研究生院及大学中心; 奥维耶多大学; 阿斯图里亚斯宇宙科学与技术大学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过几何方法将弦理论中的s规则与7膜形变的全局化障碍相联系，为T锥和五膜网提供了直接的几何联系。
AI 中文摘要
弦理论为构造和研究五维量子场论提供了强大的工具，特别是通过几何工程和五膜网。理解这两种描述在存在7膜时如何关联，需要将s规则纳入几何中。为了解决这个问题，我们聚焦于终止于7膜上的基本三腿五膜网。基于五膜终止于7膜的局部M理论描述，我们考虑具有单条非本征边的三角环面图。我们证明，当s规则被满足时，相应的局部复结构形变在相邻环面补片的重叠区域上是良定义的，而相应的粘合映射作为全纯坐标的函数在整个相邻补片上保持良行为。在饱和时，几何是一个T锥，7膜形变成为其Q-Gorenstein光滑化。因此，我们的结果将s规则等同于局部7膜形变全局化的障碍，并在T锥和终止于7膜的五膜之间提供了直接的几何联系。
英文摘要
String Theory provides powerful tools for constructing and studying five-dimensional Quantum Field Theories, notably through geometric engineering and five-brane webs. Understanding how these two descriptions are related in the presence of 7-branes requires incorporating the s-rule into the geometry. To address this question, we focus on basic three-legged five-brane webs ending on 7-branes. Building on the local M-theory description of five-branes ending on 7-branes, we consider triangular toric diagrams with a single non-primitive edge. We show that the corresponding local complex-structure deformation is well defined on the overlaps with the neighboring toric patches, while the corresponding gluing map remains well behaved as a function of the holomorphic coordinates throughout the neighboring patches precisely when the s-rule is satisfied. At saturation, the geometry is a T-cone and the 7-brane deformation becomes its Q-Gorenstein smoothing. Our results thus identify the s-rule with the obstruction to globalizing the local 7-brane deformation and provide a direct geometric link between T-cones and five-branes ending on 7-branes.
Comments20 pages, 1 figure
