论文标题
$ g_2 $ orbifold的Quark和Lepton Mass矩阵
Quark and lepton mass matrices from localization in M-theory on $G_2$ orbifold
论文作者
论文摘要
M理论在$ g_2 $歧管上压实，其解决方案$ e_8 $奇异性实现了4D $ \ MATHCAL {N} = 1 $ supersymmetric量表理论与重力与三个标准模型费米家族相连。从一个$ e_8 $奇异性开始，当$ e_8 $被几何工程变形打破到等级较小的子组时，三个费米恩家族就会出现。在本文中，我们使用该理论的局部几何形状来解释这三个家庭及其质量等级的起源。我们将与解决$ e_8 $奇异性相关的2个循环的爆炸线性化。在有效稳定的模量对有效稳定的模量上施加明确的约束后，我们到达了夸克和叶子的Yukawa耦合。我们大约适合Yukawa耦合，这使夸克群众与观察结果相当一致，这意味着在此框架内可以实现群众的实验层次结构。顶部夸克与魅力的层次结构分离和向上是一种严格的效果，而魅力和向上的吐痰也取决于希格斯行业。希格斯部门不能简化为单个VEV。所有三个VEV都必须非零。三个额外的$ u（1）$在低尺度上生存，但并非无质量，因此z'状态被激励在频谱中发生，但可能是巨大的。
M-theory compactified on a $G_2$ manifold with resolved $E_8$ singularities realizes 4d $\mathcal{N} = 1$ supersymmetric gauge theories coupled to gravity with three families of Standard Model fermions. Beginning with one $E_8$ singularity, three fermion families emerge when $E_8$ is broken by geometric engineering deformations to a smaller subgroup with equal rank. In this paper, we use the local geometry of the theory to explain the origin of the three families and their mass hierarchy. We linearize the blowing-up of 2-cycles associated with resolving $E_8$ singularities. After imposing explicit constraints on the effectively stabilized moduli, we arrive at Yukawa couplings for the quarks and leptons. We fit the high scale Yukawa couplings approximately which results in the quark masses agreeing reasonably well with the observations, implying that the experimental hierarchy of the masses is achievable within this framework. The hierarchy separation of the top quark from the charm and up is a stringy effect, while the spitting of the charm and up also depends on the Higgs sector. The Higgs sector cannot be reduced to having a single vev; all three vevs must be non-zero.Three extra $U(1)$'s survive to the low scale but are not massless, so Z' states are motivated to occur in the spectrum, but may be massive.
