论文标题
Orbifolding磁化$ T^2 \ Times T^2 $：实现$γ_n$的双重封面的实现
Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of $Γ_N$
论文作者
论文摘要
我们研究了$ T_1^2 \ times T_2^2 $和带有磁通量的Orbifold压缩的零模型的模块化对称性，$ M_1，M_2 $，其中确定了模量参数。此标识破坏了$ t^2_1 \ times t^2_2 $，$ sl（2，\ mathbb {z}）_ 1 \ times sl（2，\ mathbb {z}）_ 2 $ to $ sl（2，2，2，2，2，2，2，2，2，2，2，2，\ mathb {z}）\equivγ$。 $ t^2_1 \ times t^2_2 $和orbifolds上的每一个波函数作为主要一致性子组$γ$（$ n $）的重量1的模块化形式，是$ m_1 $和$ m_2 $的最小常见倍数的2倍。然后，零模型在模块化对称性下互相转换为$γ_n$的双覆盖组的多重组，例如$ s_4 $的双盖。
We study the modular symmetry of zero-modes on $T_1^2 \times T_2^2$ and orbifold compactifications with magnetic fluxes, $M_1,M_2$, where modulus parameters are identified. This identification breaks the modular symmetry of $T^2_1 \times T^2_2$, $SL(2,\mathbb{Z})_1 \times SL(2,\mathbb{Z})_2$ to $SL(2,\mathbb{Z})\equivΓ$. Each of the wavefunctions on $T^2_1 \times T^2_2$ and orbifolds behaves as the modular forms of weight 1 for the principal congruence subgroup $Γ$($N$), $N$ being 2 times the least common multiple of $M_1$ and $M_2$. Then, zero-modes transform each other under the modular symmetry as multiplets of double covering groups of $Γ_N$ such as the double cover of $S_4$.
