Revisiting modular symmetry in magnetized torus and orbifold compactifications
Revisiting modular symmetry in magnetized torus and orbifold compactifications
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DOI：
10.1103/physrevd.102.105010
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发表时间：
2020-05
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影响因子：
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通讯作者：
S. Kikuchi;Tatsuo C. Kobayashi;S. Takada;T. H. Tatsuishi;Hikaru Uchida
中科院分区：
文献类型：
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作者：
S. Kikuchi;Tatsuo C. Kobayashi;S. Takada;T. H. Tatsuishi;Hikaru Uchida
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 $\Gamma \equiv SL(2,\mathbb{Z})$, $\widetilde{\Gamma} \equiv \widetilde{SL}(2,\mathbb{Z})$. Each wavefunction on $T^2$ with the magnetic flux $M$ transforms under $\widetilde{\Gamma}(2|M|)$, which is the normal subgroup of $\widetilde{SL}(2,\mathbb{Z})$. Then, $|M|$ zero-modes are representations of the quotient group $\widetilde{\Gamma}'_{2|M|} \equiv \widetilde{\Gamma}/\widetilde{\Gamma}(2|M|)$. 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 $T^2$.
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 $\Gamma \equiv SL(2,\mathbb{Z})$, $\widetilde{\Gamma} \equiv \widetilde{SL}(2,\mathbb{Z})$. Each wavefunction on $T^2$ with the magnetic flux $M$ transforms under $\widetilde{\Gamma}(2|M|)$, which is the normal subgroup of $\widetilde{SL}(2,\mathbb{Z})$. Then, $|M|$ zero-modes are representations of the quotient group $\widetilde{\Gamma}'_{2|M|} \equiv \widetilde{\Gamma}/\widetilde{\Gamma}(2|M|)$. 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 $T^2$.