日本国立技术学院Tani, Taro团队研究了F理论中多重增强奇点的物质。相关论文发表在2025年3月25日出版的《高能物理杂志》上。
课题组研究了六维F理论SU（5）模型中多重增强余维两个奇点的几何结构，其中奇点的秩增加了两个或更多。他们对增强SU（5）→G′进行爆破过程，其中G′=E6、E7或E8，以检查是否出现了一组足够的异常曲线，可以解释异常抵消预测的带电物质生成。首先将六个Esole Yau小分辨率中的一个应用于乘增强奇点，但事实证明，三重方程的适当变换并不能反映奇点的变化，也不能反映广义余维两个奇点如何聚集在那里。
然后，使用一种（n）（显然）与Esole Yau不同的小分辨率方法，发现除了G′=E6的情况和E7的特殊情况外，要么（1）分辨率只产生不足以消除异常的异常曲线，要么（2）出现一种既不是二次折叠也不是广义二次折叠奇点的奇点。最后，研究组重新审视了Esole Yau的小分辨率，并表明小分辨率方式的改变相当于简单地交换适当的变换和约束条件，在这种交换下，两种小分辨率方式是完全等效的。
附：英文原文
Title: Matter from multiply enhanced singularities in F-theory
Author: Mizoguchi, Shunya, Tani, Taro
Issue&Volume: 2025-03-25
Abstract: We investigate the geometrical structure of multiply enhanced codimension-two singularities in the SU(5) model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement SU(5) → G′, where G′ = E6, E7 or E8, to examine whether a sufficient set of exceptional curves emerge that can explain the charged matter generation predicted from anomaly cancellation. We first apply one of the six Esole-Yau small resolutions to the multiply enhanced singularities, but it turns out that the proper transform of the threefold equation does not reflect changes in the singularity or how the generic codimension-two singularities gather there. We then use a(n) (apparently) different way of small resolutions than Esole-Yau to find that, except for the cases of G′ = E6 and special cases of E7, either (1) the resolution only yields exceptional curves that are insufficient to cancel the anomaly, or (2) there arises a type of singularity that is neither a conifold nor a generalized conifold singularity. Finally, we revisit the Esole-Yau small resolution and show that the change of the way of small resolutions amounts to simply exchanging the proper transform and the constraint condition, and under this exchange the two ways of small resolutions are completely equivalent.
DOI: 10.1007/JHEP03(2025)187
Source: https://link.springer.com/article/10.1007/JHEP03(2025)187