Local Discrete Symmetry in the Brane Neighborhood

With the ansatz that there exist local or global discrete symmetries in the special branes’ neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry and supersymmetry can be broken on the special branes for all the modes, and in the bulk for the zero modes by local and global discrete symmetries. To be explicit, we discuss the supersymmetric SU(5) model on $M^4\times S^1\mathrm{/}{Z}_2$ in which there is a local $Z_2^{\mathrm{\prime }}$ symmetry in the special 3-brane neighborhood along the fifth dimension.