论文标题
汽车形式和费米亚质量
Automorphic Forms and Fermion Masses
论文作者
论文摘要
我们将模块化超对称理论的框架扩展到更通用的离散组$γ$下的不变性，从而允许存在几种模量，并与自动形式的理论建立联系。 Moduli跨越了coset空间$ g/k $，其中$ g $是一个谎言组，$ k $是$ g $的紧凑型亚组，由$γ$改写。对于$ g $，$ k $，$γ$和通用物质内容的一般选择，我们明确地构建了最小的Kähler潜力和一般的超潜能，对于刚性和本地$ n = 1 $ supersympersmmetric的理论。我们还专门针对案例$ g = sp（2g，r）$，$ k = u（g）$和$γ= sp（2g，z）$，其自动形式为siegel模块化表格。我们展示了如何将我们的一般理论始终限制在模量空间的多维区域，并享有残留对称性。选择$ g = 2 $之后，我们介绍了Lepton和Quark Masses模型的几个示例，其中Yukawa耦合是2级的Siegel模块化形式。
We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $Γ$, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space $G/K$, where $G$ is a Lie group and $K$ is a compact subgroup of $G$, modded out by $Γ$. For a general choice of $G$, $K$, $Γ$ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $N=1$ supersymmetric theories. We also specialize our construction to the case $G=Sp(2g,R)$, $K=U(g)$ and $Γ=Sp(2g,Z)$, whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing $g=2$, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.
