AI 中文总结
研究将广义复曲面多边形（GTPs）的膜镶嵌推广，关注通过多面体突变与普通复曲面图相连的 GTPs。提出 $\mathcal{N}=2$ 条带凝聚，经镜像对称等验证，该凝聚能重现规范群数量，还表明 GTP 箭图与复曲面图箭图通过相关变形有关。
AI 中文摘要
广义复曲面多边形（GTPs）将 5d 超共形场理论的几何实现从复曲面卡拉比 - 丘 3 - 折扩展到终止于 7 - 膜上的一般 $(p,q)$ 5 - 膜网。我们朝着 GTPs 的膜镶嵌推广迈出了重要一步，或等效地，朝着相应的箭图理论推广。我们关注通过多面体突变与普通复曲面图相连的 GTPs。$(p,q)$ 网的平行 5 - 膜腿定义了由相应平行之字形路径界定的 $\mathcal{N}=2$ 分数膜。我们提出，在公共 7 - 膜上终止多个 5 - 膜（GTPs 的定义特征）转化为将这些之字形路径聚集在一起，从而在我们称为 $\mathcal{N}=2$ 条带凝聚的过程中将相应的 $\mathcal{N}=2$ 分数膜收缩到零尺寸。我们表明，当牛顿多项式中的系数调整到 GTP 点时，条带凝聚源于镜像对称。我们通过几个非平凡的一致性检查进一步支持这一提议。特别是，它正确地重现了预期的规范群数量，这可以等效地由与突变相关的复曲面图的数量或由 GTP 镶嵌中的 $T$ - 锥数量给出。我们对文献中先前考虑的所有例子以及具有任意大 $T$ - 锥的新的无限 GTP 族进行了验证。条带凝聚将相应的规范群驱动到无限耦合。然后禁闭产生的箭图与与突变相关的复曲面图的箭图在向量对和伴随场方面一致，这表明 GTP 箭图通过相关变形与相应复曲面图的箭图相关，将多面体突变与相关变形之间的已知对应扩展到 GTPs。
英文摘要
Generalized Toric Polygons (GTPs) extend the geometric realization of $5d$ superconformal field theories beyond toric Calabi-Yau 3-folds to general $(p,q)$ 5-brane webs ending on 7-branes. We take significant steps towards the generalization of brane tilings for GTPs, or equivalently, the corresponding quiver theories. We focus on GTPs connected to ordinary toric diagrams by polytope mutations. Parallel 5-brane legs of a $(p,q)$ web define $\mathcal{N}=2$ fractional branes bounded by the corresponding parallel zig-zag paths in the brane tiling obtained by treating the GTP as an ordinary toric diagram. We propose that terminating multiple 5-branes on a common 7-brane, the defining feature of GTPs, translates into bringing these zig-zag paths together, thereby shrinking the corresponding $\mathcal{N}=2$ fractional branes to zero size in a process we call $\mathcal{N}=2$ strip condensation. We show that strip condensation follows from mirror symmetry when the coefficients in the Newton polynomial are tuned to the GTP point. We further support this proposal through several non-trivial consistency checks. In particular, it correctly reproduces the expected number of gauge groups, given equivalently by that of the mutation-related toric diagram or by the number of $T$-cones in a tessellation of the GTP. We verify this for all examples previously considered in the literature, as well as for a new infinite family of GTPs with arbitrarily large $T$-cones. Strip condensation drives the corresponding gauge groups to infinite coupling. Confinement then yields quivers that coincide with those of the mutation-related toric diagrams up to vector pairs and adjoint fields, suggesting that GTP quivers are related to those of the corresponding toric diagrams by relevant deformations, extending to GTPs the known correspondence between polytope mutations and relevant deformations.
Comments45 pages, 30 figures
