论文标题
半hypermultiplets和F理论中的不完整/完整分辨率
Half-hypermultiplets and incomplete/complete resolutions in F-theory
论文作者
论文摘要
我们认为Codimension-Two增强的分辨率从$（12）$到$ e_7 $，从$ e_7 $到$ e_7 $到$ e_8 $在六维F理论中，其中半hypermultiplet出现了用于实现它们的通用复杂结构。如Morrison和Taylor先前观察到的，在增强点上的特殊纤维在相撞的7-Brane接近7-Branes的堆叠方面表现出不同的结构，这是从$ SU（6）$到$ e_6 $的增强。当碰撞的蓝色以$ o（s）$接近，其中$ s $是沿量规7型晶体的基本空间的坐标时，分辨率过程的最终含量少于Kodaira分类的天真纤维，而不是Kodaira分类的天真纤维，而非二氧化基相互点矩阵（包括半积分相交数字）。我们确认，相关伪真实表示的正权重的锥锥的增强点形式的特殊纤维形式，解释了为什么在那里出现半hypermultiplet。通过更改在此过程中爆炸的奇异点的顺序，我们可以获得$ SO（12）\ rightarrow e_7 $和$ e_7 \ rightarrow e_8 $，这是相应框图的每个其他行上的交点图。我们通过检查如何在奇异性增强点上的特殊纤维相交图的详细派生来研究如何在图表上抬起特殊曲线，这是由于随后的爆破过程而产生的。当碰撞的勃雷（Brane）接近Branes的堆叠为$ O（s^2）$时，我们在增强点上获得了额外的Conifold奇异性，如前所述，该点完成了增强组的完整Dynkin图。
We consider resolutions of codimension-two enhanced singularities from $SO(12)$ to $E_7$ and from $E_7$ to $E_8$ in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from $SU(6)$ to $E_6$. When the colliding brane approaches them as $O(s)$, where $s$ is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both $SO(12)\rightarrow E_7$ and $E_7\rightarrow E_8$, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as $O(s^2)$, we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously.
