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Zero-modes on orbifolds : magnetized orbifold models by modular transformation
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We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose a systematic way to analyze the number of zero-modes and their wavefunctions by use of modular transformation. Our results are consistent with the previous results, and our approach is more direct and analytical than the previous ones. The index theorem implies that the zero-mode number of the Dirac operator on $T^2$ is equal to the index $M$, which corresponds to the magnetic flux in a certain unit. Our results show that the zero-mode number of the Dirac operator on $T^2/Z_N$ is equal to $\lfloor M/N \rfloor +1$ except one case on the $T^2/Z_3$ orbifold.
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Forward citations
Cited by 2 Pith papers
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MSSM flavors from 7-brane configurations of magnetized SYM on $R^{1,3} \times (T^2)^3/(Z_2 \times Z'_2)$
Magnetized SYM on (T^2)^3/(Z_2 x Z'_2) with 7-branes, fluxes, and Wilson lines produces MSSM chiral fields and semi-realistic hierarchical Yukawas for quarks and leptons.
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Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
Blow-up of magnetized T²/Z_N preserves total magnetic flux, total curvature, and effective flux on connecting lines, while the number of localized modes at each singularity increases by one per mass level increment.
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