Tim Jeric

A bstract: We study the origin of modular weights of wave functions in magnetized T ² models. It is explicitly demonstrated that the modular weights of the wave functions on magnetized T ² are equivalent to their mass level. We further extend this result to magnetized T ^{2 g} models. As a result, we construct the wave functions of excited states in magnetized T ^{2 g} models and show that their modular weights are likewise equivalent to the corresponding mass levels.

We study fermion zero-mode wave functions with various chiralities in the magnetized T 2 g , ( g = 2 , 3 ), torus. First, we consider the wave functions satisfying the Dirac equation and the boundary conditions on the magnetized torus. Second, we introduce the S O ( 3 ) (or parity) transformations and derive the wave functions under the modular transformation. Additionally, we calculate the Yukawa couplings taking chirality into account. Lastly, we briefly review how to construct the T 4 / Z N , ( N = 2 , 3 , 4 , 6 ), and T 6 / Z 12 twisted orbifold. Also, we explicitly analyze the number of the wave functions in Z N sectors.

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional group-like selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.