Abstract
We study the modular symmetry of zero-modes on \( {T}_1^2\times {T}_2^2 \) and orbifold compactifications with magnetic fluxes, M1, M2, where modulus parameters are identified. This identification breaks the modular symmetry of \( {T}_1^2\times {T}_2^2 \), SL(2, ℤ)1 × SL(2, ℤ)2 to SL(2, ℤ) ≡ Γ. Each of the wavefunctions on \( {T}_1^2\times {T}_2^2 \) 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 M1 and M2. Then, zero-modes transform each other under the modular symmetry as multiplets of double covering groups of ΓN such as the double cover of S4.
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Kikuchi, S., Kobayashi, T., Otsuka, H. et al. Modular symmetry by orbifolding magnetized T2 × T2: realization of double cover of ΓN. J. High Energ. Phys. 2020, 101 (2020). https://doi.org/10.1007/JHEP11(2020)101
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DOI: https://doi.org/10.1007/JHEP11(2020)101