论文标题
重新访问磁化圆环和轨道压缩中的模块化对称性
Revisiting modular symmetry in magnetized torus and orbifold compactifications
论文作者
论文摘要
我们研究$ t^2 $的模块化对称性，以及与磁通量的Orbifold Comfactification。 $ | m | $ $零模型在$ t^2 $上带有磁性磁通$ m $。它们的波形和大量模式的举止是重量$ 1/2 $的模块化形式，代表$γ\ equiv sl的双覆盖组（2，\ mathbb {z}）$，$ \ wideTildeldeldeldeldeldectelg \ equiv \ equiv \ wideTilde {sl}（sl}（2，2，\ m m mathbb {z}）$。 $ t^2 $上的每个波函数与磁性通量$ m $在$ \widetildeγ（2 | m |）$下转换，这是$ \ widetilde {sl}（2，\ mathbb {z}）$的普通子组。然后，$ | M | $零模型是商组的表示形式$ \widetildeγ'_ {2 | M |} \ equiv \ equiv \wideTildeγ/\ widetildec（2 | m |）$。我们还研究了扭曲和移动的Orbifolds上的模块化对称性，$ t^2/\ mathbb {z} _n $。通过扭曲和移位的特征值将波形分解为较小的表示。他们为我们提供了$ t^2 $的可简化表示形式。
We study the modular symmetry in $T^2$ and orbifold comfactifications with magnetic fluxes. There are $|M|$ zero-modes on $T^2$ with the magnetic flux $M$. Their wavefunctions as well as massive modes behave as modular forms of weight $1/2$ and represent the double covering group of $Γ\equiv SL(2,\mathbb{Z})$, $\widetildeΓ \equiv \widetilde{SL}(2,\mathbb{Z})$. Each wavefunction on $T^2$ with the magnetic flux $M$ transforms under $\widetildeΓ(2|M|)$, which is the normal subgroup of $\widetilde{SL}(2,\mathbb{Z})$. Then, $|M|$ zero-modes are representations of the quotient group $\widetildeΓ'_{2|M|} \equiv \widetildeΓ/\widetildeΓ(2|M|)$. We also study the modular symmetry on twisted and shifted orbifolds $T^2/\mathbb{Z}_N$. Wavefunctions are decomposed into smaller representations by eigenvalues of twist and shift. They provide us with reduction of reducible representations on $T^2$.
