Strings on orbifolds

As discussed in the previous chapter, the heterotic string possesses very rich symmetries. It naturally describes SO(32) and E₈ ×E₈ gauge group, by assigned charges along the string. Also it has sixteen real (N = 4 in four dimension) supersymmetries. However, these symmetries are too large from the phenomenological point of view, by the criteria discussed in Chap. 2. Namely, in weakly coupled string theories, unless the fortuitous appearance of family structure results from the twisted sector as we will see it is better for a big gauge group is given already so that the standard model(SM) gauge group of rank 4 can be embedded there. In addition, as emphasized in Chap. 2, the group must allow "spinor representation" of SO(10). This leads to the E₈ ×E′₈ heterotic string as the first choice. In a strongly coupled string, nonperturbative effects may produce defects and we have to consider branes also. Compactification of strongly coupled strings are briefly sketched in Appendix B.2.