Modular symmetry in magnetized T2g torus and orbifold models

We study the modular symmetry in magnetized T2g torus and orbifold models. The T2g torus has the modular symmetry Γg=Sp(2g,Z). The magnetic flux background breaks the modular symmetry to a certain normalizer Ng(H). We classify remaining modular symmetries by magnetic flux matrix types. Furthermore, we study the modular symmetry for wave functions on the magnetized T2g and certain orbifolds. It is found that wave functions on magnetized T2g as well as its orbifolds behave as the Siegel modular forms of weight 1/2 and N˜g(H,h), which is the metaplectic congruence subgroup of the double covering group of Ng(H), N˜g(H). Then, wave functions transform nontrivially under the quotient group, N˜g,h=N˜g(H)/N˜g(H,h), where the level h is related to the determinant of the magnetic flux matrix. Accordingly, the corresponding four-dimensional chiral fields also transform nontrivially under N˜g,h modular flavor transformation with modular weight −1/2. We also study concrete modular flavor symmetries of wave functions on magnetized T2g orbifolds. Published by the American Physical Society 2024